PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

\[\int\limits_0^1 \cot^{- 1} \left( 1 - x + x^2 \right) dx\]

\[\int\limits_0^\pi \frac{dx}{6 - \cos x}dx\]

\[\int\limits_0^{\pi/2} \frac{1}{2 \cos x + 4 \sin x} dx\]

\[\int\limits_{\pi/6}^{\pi/2} \frac{\ cosec x \cot x}{1 + {cosec}^2 x} dx\]

\[\int\limits_0^{\pi/2} \frac{dx}{4 \cos x + 2 \sin x}dx\]

\[\int\limits_0^4 x dx\]

\[\int\limits_0^2 \left( 2 x^2 + 3 \right) dx\]

\[\int\limits_1^4 \left( x^2 + x \right) dx\]

\[\int\limits_{- 1}^1 e^{2x} dx\]

\[\int\limits_2^3 e^{- x} dx\]

\[\int\limits_1^3 \left( 2 x^2 + 5x \right) dx\]

\[\int\limits_1^3 \left( x^2 + 3x \right) dx\]

\[\int\limits_0^2 \left( x^2 + 2 \right) dx\]

\[\int\limits_0^3 \left( x^2 + 1 \right) dx\]

If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`

If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`

Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=0`

Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`

Evaluate `∫_0^(3/2)|x cosπx|dx`

Evaluate :

`∫_(-pi)^pi (cos ax−sin bx)^2 dx`

If `int_0^a1/(4+x^2)dx=pi/8` , find the value of a.