Integrals: CBSE Class 12 Previous Year Questions

If $\int \frac{3ax}{b^2+c^2{x}^2}dx=A\log \left|b^2+c^2{x}^2\right|+K$, then the value of A is

1. (A)3a
2. (B)$\frac{3a}{2b^2}$
3. (C)$\frac{3a}{b^2{c}^2}$
4. (D)$\frac{3a}{2c^2}$

The value of ${\int }_{-1}^1\frac{x^3}{x^2+2|x|+1}dx$ is

1. (A)0
2. (B)$\log 2$
3. (C)$2\log 2$
4. (D)$\frac{1}{2}\log 2$

${\int }_{-1}^1(1-|x|)dx$ is equal to :

1. (A)$2{\int }_0^1(1+x)dx$
2. (B)$2{\int }_{-1}^0(1+x)dx$
3. (C)$0$
4. (D)$2{\int }_{-1}^0(1-x)dx$

$\int \frac{dx}{\sqrt{25-16x^2}}$ is equal to :

1. (A)$\frac{1}{5}{\sin }^{-1}4x+C$
2. (B)$\frac{1}{25}{\sin }^{-1}16x+C$
3. (C)$\frac{1}{4}{\sin }^{-1}\frac{4x}{5}+C$
4. (D)$\frac{1}{16}{\sin }^{-1}\frac{4x}{5}+C$

If ${\int }_0^1\frac{dx}{e^x+e^{-x}}={\tan }^{-1}e+k$, then the value of k is :

1. (A)e
2. (B)$\frac{\pi }{4}$
3. (C)0
4. (D)$-\frac{\pi }{4}$

Find $\int \sqrt{\frac{x+2}{x-2}}dx$

Find : $\int \frac{x^2}{(x^2+9)(x^2+16)}dx$

If $I_1={\int }_{-\pi /4}^{\pi /4}\frac{dx}{1+\cos 2x}$ and $I_2={\int }_{-1/2}^{1/2}|x|dx$, then show that $I_1-4I_2=0$.

Evaluate : ${\int }_{\frac{\pi }{12}}^{\frac{5\pi }{12}}\frac{dx}{1+\sqrt{\cot x}}$

Evaluate : ${\int }_{\frac{-\pi }{6}}^{\frac{\pi }{2}}(\sin |x|+\cos |x|)dx$