NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.5

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NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.5 is covered in this article. Exercise 7.5 covers questions on the topic, Integration by Substitution, Integration using Partial Fractions, Integration by Parts. NCERT Solutions for Class 12 Maths Chapter 7 will carry a weightage of around 6-18 marks in the CBSE Term 2 Exam 2022. NCERT has provided a total of 23 problems and solutions based on the important topics.

Download PDF NCER Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.5

NCERT Solutions for Class 12 Maths Chapter 7: Important Topics

Important topics covered in Integrals Chapter are:

Double Integral
Continuous Integration
Properties of Definite Integral
Line Integral
Integrals of Particular Function

Also check: NCERT Solutions for Class 12 Maths Chapter 7 Integrals

CBSE CLASS XII Related Questions

1.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]
View Solution
2.
If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
\[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]
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3.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]
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4.
The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that
(i) target is hit.
(ii) at least one shot misses the target.
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5.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.
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6.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following:

(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).
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Mathematics NCERT Solutions

NCERT Solutions For Class 12 Mathematics Chapter 13: Probability

NCERT Solutions For Class 12 Mathematics Chapter 9: Differential Equations

NCERT Solutions For Class 12 Mathematics Chapter 7 Integrals

NCERT Solutions For Class 12 Mathematics Chapter 12: Linear Programming

NCERT Solutions for Class 12 Maths Chapter 3 Matrices

NCERT Solutions For Class 12 Mathematics Chapter 6 Applications of Derivatives

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You can also check

Exercise 7.1 Solutions	22 Questions
Exercise 7.2 Solutions	39 Questions
Exercise 7.3 Solutions	24 Questions
Exercise 7.4 Solutions	25 Questions
Exercise 7.5 Solutions	23 Questions
Exercise 7.6 Solutions	24 Questions
Exercise 7.7 Solutions	11 Questions
Exercise 7.8 Solutions	6 Questions
Exercise 7.9 Solutions	22 Questions
Exercise 7.10 Solutions	10 Questions
Exercise 7.11 Solutions	21 Questions
Miscellaneous Exercise Solutions	44 Questions

Methods of Integration	List of Integral Formulas	Double Integral
Fundamental Theorem of Calculus	Integration by Partial Fractions	Definite Integral Formula
Continuous integration	Properties of Definite Integral	Line Integral
Calculus Formula	Differentiation and Integration Formula	Substitution Method

NCERT Solutions for Class 12 Maths	Maths MCQs	Maths Syllabus
Arithmetic	Calculus	Algebra
Mathematics Notes	Trigonometry	Maths Study Material

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.5

NCERT Solutions for Class 12 Maths Chapter 7: Important Topics

Other Exercises Solutions of Class 12 Maths Chapter 7 Integrals

CBSE CLASS XII Related Questions

1.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]

3.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

5.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

Similar Mathematics Concepts

Comments

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NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.5

NCERT Solutions for Class 12 Maths Chapter 7: Important Topics

Other Exercises Solutions of Class 12 Maths Chapter 7 Integrals

CBSE CLASS XII Related Questions

1.Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]

3.Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

5.A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]

3.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

5.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.