The value of \int_{0}^{\pi \/ 4} x \cos (x^{2}) d x correct to three decimal places (assuming that \pi=3.14) is

GATE Computer Science (CS) 2018 Shift 1 Solved Paper

Question : 19 of 65

Marks: +1, -0

The value of

∫↙{0}↖{π \/ 4} x \cos (x^{2}) d x

correct to three decimal places (assuming that

π=3.14)

Solution:

∫↙{0}↖{x{/ }4} x \cos (x^{2}) \dx

Let,

t=x^{2}

d t=2 x \dx

⇒x d x=\;{\dt}/{2}

when

x=0, t=0

and when

x=\;{π}/{4}, t=(\;{π}/{4})^{2}

So required integral reduce to

∫↙{0}^{(x {/}4)^{2}} \cos t d t=[\sin t]_{0}^{(z{/} 4)^{2}}

=\sin (\;{π}/{4})^{2}-\sin (0)

=\sin (\;{π}/{4})^{2}=0.28898

Go to Question:

Prev Question

Next Question