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Mathematics
Mathematics
Problem
Answer the following questions related to the integral involving a trigonometric function. a. (i) Evaluate the indefinite integral
∫
x
cos
(
x
2
)
d
x
\displaystyle \int x\,\cos\bigl(x^{2}\bigr)\,dx
∫
x
cos
(
x
2
)
d
x
. b. (ii) Hence determine
∫
0
π
x
cos
(
x
2
)
d
x
\displaystyle \int_{0}^{\sqrt{\pi}} x\,\cos\bigl(x^{2}\bigr)\,dx
∫
0
π
x
cos
(
x
2
)
d
x
.
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