TS EAMCET PYQs for Methods of Integration with Solutions: Practice TS EAMCET Previous Year Questions

Updated 3+ months ago

Methods of Integration is an important topic in the Mathematics section in TS EAMCET exam. Practising this topic will increase your score overall and make your conceptual grip on TS EAMCET exam stronger.

This article gives you a full set of TS EAMCET PYQs for Methods of Integration with explanations for effective preparation. Practice of TS EAMCET Mathematics PYQs including Methods of Integration questions regularly will improve accuracy, speed, and confidence in the TS EAMCET 2026 exam.

TS EAMCET PYQs for Methods of Integration with Solutions

1.
If \( f(x) = kx^3 - 3x^2 - 12x + 8 \) is strictly decreasing for all \( x \in \mathbb{R} \), then:
- \( k<-\frac{1}{4} \)
- \( k>-\frac{1}{4} \)
- \( k>\frac{1}{4} \)
- \( k<\frac{1}{4} \)
View Solution
2.
Evaluate the integral: \[ \int \frac{dx}{9\cos^2 2x + 16\sin^2 2x} \]
- \( \frac{1}{25} \tan^{-1} \left( \frac{3}{4} \sec^2 2x \right) + c \)
- \( \frac{1}{25} \tan^{-1} \left( \frac{4}{3} \sec^2 2x \right) + c \)
- \( \frac{1}{24} \tan^{-1} \left( \frac{3}{4} \tan 2x \right) + c \)
- \( \frac{1}{24} \tan^{-1} \left( \frac{4}{3} \tan 2x \right) + c \)
View Solution
3.
Evaluate the integral: \[ I = \int_{\frac{-3\pi}{4}}^{\frac{\pi}{6}} \log(\sin(4x+3)) \,dx \]
- \( -\frac{\pi}{2} \log 2 \)
- \( -\frac{\pi}{8} \log 2 \)
- \( -\frac{\pi}{14} \log 2 \)
- \( -\frac{\pi}{28} \log 2 \)
View Solution
4.
If \( \int x^3 \sin 3x \,dx = f(x) \cos 3x + g(x) \sin 3x + c \), then evaluate \( 27(f(x) + xg(x)) \):
- \( 18x^3 + 4x \)
- \( 8x \)
- \( 4x \)
- \( 18x^3 + 8x \)
View Solution
5.
Evaluate the integral: \[ \int \left( \sin^3 x + \cos^2 x \right)^2 \, dx \]
- \( \frac{15 \pi}{16} + \frac{8}{15} \)
- \( \frac{11 \pi}{16} + \frac{8}{15} \)
- \( \frac{15 \pi}{16} + \frac{4}{15} \)
- \( \frac{11 \pi}{16} + \frac{4}{15} \) \bigskip
View Solution
6.
Evaluate the integral: \[ \int (\log x)^3 \, dx \]
- \( ( \log x)^3 - 3 (\log x)^2 + 6 \log x - 6 + c \)
- \( x [ (\log x)^3 - 3 (\log x)^2 + 6 \log x - 6 ] + c \)
- \( (x \log x)^3 - 3 (x \log x)^2 + 6x \log x - 6x + c \)
- \( x [ (\log x)^3 - 3 (\log x)^2 + 6 \log x - 6 ] + c \) \bigskip
View Solution
7.
Evaluate the integral: \[ \int e^{-2x} \left( \tan 2x - 2\sec^2 2x \tan 2x \right) dx. \]
- \( e^{-2x} \tan 2x + c \)
- \( -\frac{e^{-2x}}{2} \left[ \sec^2 2x + \tan 2x \right] + c \)
- \( -\frac{e^{-2x}}{2} \left[ \tan 2x - \sec^2 2x \right] + c \)
- \( -e^{-2x} \sec^2 2x + c \)
View Solution
8.
A right circular cone is inscribed in a sphere of radius 3 units. If the volume of the cone is maximum, then the semi-vertical angle of the cone is:
- \( \frac{\pi}{4} \)
- \( \frac{\pi}{6} \)
- \( \tan^{-1} (\sqrt{2}) \)
- \( \tan^{-1} \left(\frac{1}{\sqrt{2}}\right) \)
View Solution
9.
Evaluate the integral: \[ \int \frac{4\tan^4 x + 3 \tan^2 x - 1}{\tan^2 x + 4} \, dx. \]
- \( 4 \tan x - \frac{17}{4} \tan ^{-1} \frac{tan x}{4} \)
- \( 4 \tan x - \frac{17}{4} \tan ^{-1} \frac{tan x}{2} \)
- \( 4 \tan x - \frac{17}{2} \tan ^{-1} \frac{tan x}{2} \)
- \( 2 \tan x - \frac{17}{2} \tan ^{-1} \frac{tan x}{2} \) \bigskip
View Solution
10.
Evaluate the integral: \[ \int \frac{(\sin^4x + 2\cos^2x - 1) \cos x}{(1 + \sin x)^6} \, dx \]
- \( \frac{\sin^6 x}{6(1 + \sin x)^6} + c \)
- \( - \frac{\sin^6 x}{6(1 + \sin x)^6} + c \)
- \( \frac{\cos^6 x}{6(1 + \sin x)^6} + c \)
- \( - \frac{\cos^6 x}{6(1 + \sin x)^6} + c \) \bigskip
View Solution
11.
The area of the region enclosed by the curves \( y^2 = 4(x+1) \) and \( y^2 = 5(x-4) \) is:
- \( \frac{280}{3} \)
- 150
- 140
- \( \frac{200}{3} \) \bigskip
View Solution
12.
Evaluate the integral: \[ I = \int_{-\frac{\pi}{8}}^{\frac{\pi}{8}} \frac{\sin^4(4x)}{1 + e^{4x}} \, dx \]
- \( \frac{3\pi}{128} \)
- \( \frac{3\pi}{256} \)
- \( \frac{3\pi}{64} \)
- \( \frac{3\pi}{32} \) \bigskip
View Solution
13.
Evaluate the integral: \[ \int \frac{2\cos 3x - 3\sin 3x}{\cos 3x + 2\sin 3x} dx. \]
- \( \frac{7}{15} \log |\cos 3x + 2\sin 3x| - \frac{4}{5} x + c \)
- \( -\frac{4}{5} \log |\cos 3x + 2\sin 3x| + \frac{7x}{5} + c \)
- \( \frac{7}{5} \log |\cos 3x + 2\sin 3x| - \frac{4}{5} x + c \)
- \( -\frac{8}{15} \log |\cos 3x + 2\sin 3x| + \frac{x}{5} + c \)
View Solution
14.
Evaluate the integral: \[ I = \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \,dx \]
- \( 16\sqrt{2} \)
- \( 32\sqrt{2} \)
- \( 128\sqrt{2} \)
- \( 64\sqrt{2} \)
View Solution
15.
Evaluate the integral: \[ \int_0^{16} \frac{\sqrt{x}}{1 + \sqrt{x}} dx. \]
- \( 8 + 2\log 2 \)
- \( 8 + \log 2 \)
- \( 8 + 2\log 5 \)
- \( 8 + \log 5 \)
View Solution

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TS EAMCET PYQs for Methods of Integration with Solutions: Practice TS EAMCET Previous Year Questions

TS EAMCET PYQs for Methods of Integration with Solutions

1.
If \( f(x) = kx^3 - 3x^2 - 12x + 8 \) is strictly decreasing for all \( x \in \mathbb{R} \), then:

2.
Evaluate the integral: \[ \int \frac{dx}{9\cos^2 2x + 16\sin^2 2x} \]

3.
Evaluate the integral: \[ I = \int_{\frac{-3\pi}{4}}^{\frac{\pi}{6}} \log(\sin(4x+3)) \,dx \]

4.
If \( \int x^3 \sin 3x \,dx = f(x) \cos 3x + g(x) \sin 3x + c \), then evaluate \( 27(f(x) + xg(x)) \):

5.
Evaluate the integral: \[ \int \left( \sin^3 x + \cos^2 x \right)^2 \, dx \]

6.
Evaluate the integral: \[ \int (\log x)^3 \, dx \]

7.
Evaluate the integral: \[ \int e^{-2x} \left( \tan 2x - 2\sec^2 2x \tan 2x \right) dx. \]

8.
A right circular cone is inscribed in a sphere of radius 3 units. If the volume of the cone is maximum, then the semi-vertical angle of the cone is:

9.
Evaluate the integral: \[ \int \frac{4\tan^4 x + 3 \tan^2 x - 1}{\tan^2 x + 4} \, dx. \]

10.
Evaluate the integral: \[ \int \frac{(\sin^4x + 2\cos^2x - 1) \cos x}{(1 + \sin x)^6} \, dx \]

11.
The area of the region enclosed by the curves \( y^2 = 4(x+1) \) and \( y^2 = 5(x-4) \) is:

12.
Evaluate the integral: \[ I = \int_{-\frac{\pi}{8}}^{\frac{\pi}{8}} \frac{\sin^4(4x)}{1 + e^{4x}} \, dx \]

13.
Evaluate the integral: \[ \int \frac{2\cos 3x - 3\sin 3x}{\cos 3x + 2\sin 3x} dx. \]

14.
Evaluate the integral: \[ I = \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \,dx \]

15.
Evaluate the integral: \[ \int_0^{16} \frac{\sqrt{x}}{1 + \sqrt{x}} dx. \]

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TS EAMCET PYQs for Methods of Integration with Solutions

1.If \( f(x) = kx^3 - 3x^2 - 12x + 8 \) is strictly decreasing for all \( x \in \mathbb{R} \), then:

2.Evaluate the integral: \[ \int \frac{dx}{9\cos^2 2x + 16\sin^2 2x} \]

3.Evaluate the integral: \[ I = \int_{\frac{-3\pi}{4}}^{\frac{\pi}{6}} \log(\sin(4x+3)) \,dx \]

4.If \( \int x^3 \sin 3x \,dx = f(x) \cos 3x + g(x) \sin 3x + c \), then evaluate \( 27(f(x) + xg(x)) \):

5.Evaluate the integral: \[ \int \left( \sin^3 x + \cos^2 x \right)^2 \, dx \]

6.Evaluate the integral: \[ \int (\log x)^3 \, dx \]

7.Evaluate the integral: \[ \int e^{-2x} \left( \tan 2x - 2\sec^2 2x \tan 2x \right) dx. \]

8.A right circular cone is inscribed in a sphere of radius 3 units. If the volume of the cone is maximum, then the semi-vertical angle of the cone is:

9.Evaluate the integral: \[ \int \frac{4\tan^4 x + 3 \tan^2 x - 1}{\tan^2 x + 4} \, dx. \]

10.Evaluate the integral: \[ \int \frac{(\sin^4x + 2\cos^2x - 1) \cos x}{(1 + \sin x)^6} \, dx \]

11.The area of the region enclosed by the curves \( y^2 = 4(x+1) \) and \( y^2 = 5(x-4) \) is:

12.Evaluate the integral: \[ I = \int_{-\frac{\pi}{8}}^{\frac{\pi}{8}} \frac{\sin^4(4x)}{1 + e^{4x}} \, dx \]

13.Evaluate the integral: \[ \int \frac{2\cos 3x - 3\sin 3x}{\cos 3x + 2\sin 3x} dx. \]

14.Evaluate the integral: \[ I = \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \,dx \]

15.Evaluate the integral: \[ \int_0^{16} \frac{\sqrt{x}}{1 + \sqrt{x}} dx. \]

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1.
If \( f(x) = kx^3 - 3x^2 - 12x + 8 \) is strictly decreasing for all \( x \in \mathbb{R} \), then:

2.
Evaluate the integral: \[ \int \frac{dx}{9\cos^2 2x + 16\sin^2 2x} \]

3.
Evaluate the integral: \[ I = \int_{\frac{-3\pi}{4}}^{\frac{\pi}{6}} \log(\sin(4x+3)) \,dx \]

4.
If \( \int x^3 \sin 3x \,dx = f(x) \cos 3x + g(x) \sin 3x + c \), then evaluate \( 27(f(x) + xg(x)) \):

5.
Evaluate the integral: \[ \int \left( \sin^3 x + \cos^2 x \right)^2 \, dx \]

6.
Evaluate the integral: \[ \int (\log x)^3 \, dx \]

7.
Evaluate the integral: \[ \int e^{-2x} \left( \tan 2x - 2\sec^2 2x \tan 2x \right) dx. \]

8.
A right circular cone is inscribed in a sphere of radius 3 units. If the volume of the cone is maximum, then the semi-vertical angle of the cone is:

9.
Evaluate the integral: \[ \int \frac{4\tan^4 x + 3 \tan^2 x - 1}{\tan^2 x + 4} \, dx. \]

10.
Evaluate the integral: \[ \int \frac{(\sin^4x + 2\cos^2x - 1) \cos x}{(1 + \sin x)^6} \, dx \]

11.
The area of the region enclosed by the curves \( y^2 = 4(x+1) \) and \( y^2 = 5(x-4) \) is:

12.
Evaluate the integral: \[ I = \int_{-\frac{\pi}{8}}^{\frac{\pi}{8}} \frac{\sin^4(4x)}{1 + e^{4x}} \, dx \]

13.
Evaluate the integral: \[ \int \frac{2\cos 3x - 3\sin 3x}{\cos 3x + 2\sin 3x} dx. \]

14.
Evaluate the integral: \[ I = \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \,dx \]

15.
Evaluate the integral: \[ \int_0^{16} \frac{\sqrt{x}}{1 + \sqrt{x}} dx. \]