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  • Explain solution RD Sharma class 12 Chapter 19 Definite Integrals Exercise Revision Exercise question 55

Explain solution RD Sharma class 12 Chapter 19 Definite Integrals Exercise Revision Exercise question 55

Answers (1)

Answer:  0

Hint: In this equation we use  f\left ( x \right )= -f\left ( x \right )

Given:  \int_{-\pi}^{\pi} x^{10} \sin ^{7} x d x

Solution:

\begin{aligned} &I=f(x) \Rightarrow-f(x) \\ & \end{aligned}

\int_{-a}^{a} f(x) d x=0 \\

I=\int_{-\pi}^{\pi} x^{10} \sin ^{7} x d x

\begin{aligned} &I=\int_{-\pi}^{\pi} x^{10} \sin ^{7} x d x \\ & \end{aligned}

f(x)=x^{10} \sin ^{7} x d x \\

\begin{aligned} &f(-x)=(-x)^{10} \sin ^{7}(-x) d x \\ & \end{aligned}

f(-x)=-x^{10} \sin ^{7} x \\

f(-x)=-f(x) \\

\int_{-a}^{a} f(x) d x=0 \\

\int_{-\pi}^{\pi} x^{10} \sin ^{7} x d x=0

 

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