Arts (English Medium) Class 12 - CBSE Question Bank Solutions

Evaluate:\[\int\frac{\sin \sqrt{x}}{\sqrt{x}} \text{ dx }\]

Evaluate:\[\int\frac{\cos \sqrt{x}}{\sqrt{x}} \text{ dx }\]

Evaluate:\[\int\frac{\left( 1 + \log x \right)^2}{x} \text{   dx }\]

Evaluate:\[\int \sec^2 \left( 7 - 4x \right) \text{ dx }\]

Evaluate:\[\int\frac{\log x}{x} \text{ dx }\]

Evaluate:  \[\int 2^x  \text{ dx }\]

Evaluate: \[\int\frac{x^3 - x^2 + x - 1}{x - 1} \text{ dx }\]

Evaluate:\[\int\frac{e\tan^{- 1} x}{1 + x^2} \text{ dx }\]

Evaluate: \[\int\frac{1}{\sqrt{1 - x^2}} \text{ dx }\]

Write the value of\[\int\sec x \left( \sec x + \tan x \right)\text{  dx }\]

Evaluate: \[\int\frac{1}{x^2 + 16}\text{ dx }\]

Evaluate: \[\int\left( 1 - x \right)\sqrt{x}\text{  dx }\]

Evaluate: \[\int\frac{x + \cos6x}{3 x^2 + \sin6x}\text{ dx }\]

Evaluate:  \[\int\frac{2}{1 - \cos2x}\text{ dx }\]

Evaluate:

\[\int \cos^{-1} \left(\sin x \right) \text{dx}\]

Evaluate:

`∫ (1)/(sin^2 x cos^2 x) dx`

Evaluate : \[\int\frac{1}{x(1 + \log x)} \text{ dx}\]

Find the coordinates of the point where the line  \[\frac{x - 2}{3} = \frac{y + 1}{4} = \frac{z - 2}{2}\]   intersects the plane x − y + z − 5 = 0. Also, find the angle between the line and the plane. 

Find the distance of the point (−1, −5, −10) from the point of intersection of the line \[\vec{r} = \left( 2 \hat{i}  - \hat{j} + 2 \hat{k}  \right) + \lambda\left( 3 \hat{i}+ 4 \hat{j} + 2 \hat{k}  \right)\] and the plane  \[\vec{r} . \left( \hat{i}  - \hat{j}  + \hat{k} \right) = 5 .\]