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Question

Question: \(\int_{0}^{\pi/2}{\sin^{7}xdx}\) has value...

∫0π/2sin⁡7xdx\int_{0}^{\pi/2}{\sin^{7}xdx} has value

A

37184\frac{37}{184}

B

1745\frac{17}{45}

C

1635\frac{16}{35}

D

1645\frac{16}{45}

Answer

1635\frac{16}{35}

Explanation

Solution

Using Walli’s formula, ⇒

I=7−17.7−37−2.7−57−4=6.4.27.5.3=1635I = \frac{7 - 1}{7}.\frac{7 - 3}{7 - 2}.\frac{7 - 5}{7 - 4} = \frac{6.4.2}{7.5.3} = \frac{16}{35}