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

Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]

Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].

Write a value of\[\int e^{ax} \sin\ bx\ dx\]

Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .

Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .

Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]

Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].

Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]

Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]

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

The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is

The value of \[\int\frac{1}{x + x \log x} dx\] is

\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]

Verify Rolle's theorem for the following function on the indicated interval f(x) = x² − 8x + 12 on [2, 6] ?

Verify Rolle's theorem for the following function on the indicated interval f(x) = x² − 4x + 3 on [1, 3] ?

Verify Rolle's theorem for the following function on the indicated interval f (x) = (x − 1) (x − 2)² on [1, 2] ?

Verify Rolle's theorem for the following function on the indicated interval  f (x) = x(x − 1)² on [0, 1] ?