NCERT Solutions for Applications of Integrals Exercise 8.1 Solutions

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Class 12 Maths NCERT Solutions Chapter 8 Applications of Integrals Exercise 8.1 is provided in the article. Class 12 Chapter 8 Applications of Integrals Exercises include questions on area between a curve, parabola, and ellipse.

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CBSE CLASS XII Related Questions

  • 1.
    Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]


      • 2.
        Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]


          • 3.
            Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).


              • 4.
                Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.


                  • 5.
                    Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]


                      • 6.
                        Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

                          CBSE CLASS XII Previous Year Papers

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