Indefinite Integrals - Class 12 Commerce Applied Mathematics - Extra Questions
Integrate the following function with respect to x. xsinhx
Solve :
a∫0√x√x+√a−xdx
The value of (∫x.e−xdx) is,
The integration of y=x22+c . What does c represent?
I=∫ex(2cos2x+2sinxcosxcos2x)dx
Integrate the function xsinx
Evaluate ∫x2exdx.
Object: ∫cosec−1x,dx,x>1.
The acceleration of a particle varies with time t seconds according to the relation a = 6t + 6\ ms^{-2}. Find velocity and position as functions of time. It is given that the particle starts from origin at t = 0 with velocity 2\ ms^{-1}.
Prove that \displaystyle \int x^{2}a^{x}dx=\frac{a^{x}}{\left ( \log a \right )^{3}}\left [ x^{2}\left ( \log a \right )^{2}-2x\left ( \log a \right )+2 \right ].
\displaystyle\int x^{3}\left ( \log x \right )^{2}dx=\frac{x^{4}}{4}\left ( \log x \right )^{2}-\frac{1}{8}x^{4}\log x+\frac{1}{4k}x^{4}. Find the value of k
Show that \displaystyle \int \left ( e^{\log x}+\sin x \right )\cos dx=x\sin x+\cos x+\frac{1}{2}\sin^{2}x.
\displaystyle \int \left [ \frac{1}{\log x}-\frac{1}{\left ( \log x \right )^{2}} \right ]dx=x \left ( \log x \right )^{-1}. If this is true enter 1, else enter 0.
Show that \int \displaystyle x\sin x\cos x = f(x), taking const. of integration as zero. Find f(\pi /4)
\displaystyle \int \sec ^{2}x\log \left ( 1+\sin^{2}x \right )dx=\tan x\log \left ( 1+\sin ^{2}x \right )-2x+\sqrt{k}\tan^{-1}\sqrt{k}\tan x. Find the value of k.
The value of \displaystyle\int{{e}^{\ln{\sqrt{x}}}dx} is
Find the integrals of the functions. i) sin^2 (2x + 5) ii) sin \, 3x \, cos \, 4x iii) cos \, 2x \, cos \, 4x \, cos \, 6x iv) sin^3 (2x + 1)
Find the integrals of the functions. i) sin^3 \, x \, cos^3 \, x ii) sin \, x \, sin \, 2x \, sin \, 3x iii) sin \, 4x \, sin \, 8x iv) \dfrac{1 - cos \, x}{1 + cos \, x} v) \dfrac{cos \, x}{1 + cos \, x}
\displaystyle \int xe^{x}\cos x dx=\frac{e^{x}}{2}\left [ \left ( x-1 \right )\sin x+x\cos x \right ]. If this is true enter 1, else enter 0.
f the graph of the antiderivative F(x) of \displaystyle f\left ( x \right )=\log \left ( \log x \right )+\left ( \log x \right )^{-2} passes through (e, 1998-e) then the term independent of x in F(x) is
\displaystyle \int \sqrt{x^{6}+1}.\frac{\log \left ( x^{6}+1 \right )-6\log x}{x^{10}}dx=\frac{1}{6}\left [ \frac{2}{3}t^{3/2}\log t -\frac{2}{3}\int t^{3/2}\frac{1}{t} \right ] where t=1+\frac{1}{x^{6}}. If this is true enter 1, else enter 0.