Let y = y(x) and (1 + x^2 )y′ – 2xy = (x^4 + 2x^2 + 1) cosx.

Question

Let y = y(x) and  \(\left(1+x^{2}\right) y^{\prime}-2 x y=\left(x^{4}+2 x^{2}+1\right) \cos x.\)

If y(0) = 1, then \(\int_\limits{-3}^{3} y(x) d x\) equals to

(1) 20

(2) 15

(3) 24

(4) 10

Answer 1

Correct option is: (3) 24 

\(=\int_\limits{0}^{3} 2\left(1+x^{2}\right) d x\)

\(\left.=2 x+\frac{2 x^{3}}{3}\right]_{0}^{3}\)

= 6 + 18 = 24