# Evaluate the integral \int_0^{\frac{π^2}{4}} \frac{9 sin⁡\sqrt{x}}{2\sqrt{x}} dx.

Category: QuestionsEvaluate the integral \int_0^{\frac{π^2}{4}} \frac{9 sin⁡\sqrt{x}}{2\sqrt{x}} dx.
Editor">Editor Staff asked 11 months ago

Evaluate the integral \int_0^{\frac{π^2}{4}} \frac{9 sin⁡\sqrt{x}}{2\sqrt{x}} dx
.

(a) 9

(b) -9

(c) \frac{9}{2}

(d) –\frac{9}{2}

This question was posed to me in examination.

The above asked question is from Evaluation of Definite Integrals by Substitution in section Integrals of Mathematics – Class 12
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Editor">Editor Staff answered 11 months ago

The explanation: I=

π
2
4
0
9sin
x

2
x

dx

Let
x

=t

Differentiating both sides w.r.t x, we get

1
2
x

dx=dt

The new limits are

When x=0 , t=0

When x=
π
2
4
,t=
π
2

π
2
4
0
9sin
x

2
x

dx=9

π/2
0
sintdt

=
9[−cost
]
π/2
0
=-9(cos⁡ π/2-cos⁡0)=-9(0-1)=9