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

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

Evaluate `∫_0^(3/2)|x cosπx|dx`

Show that four points A, B, C and D whose position vectors are 

`4hati+5hatj+hatk,-hatj-hatk-hatk, 3hati+9hatj+4hatk and 4(-hati+hatj+hatk)` respectively are coplanar.

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 :

`∫_(-pi)^pi (cos ax−sin bx)^2 dx`

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

Evaluate :

`int_e^(e^2) dx/(xlogx)`

Evaluate of the following integral:

(i)  \[\int x^4 dx\]

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