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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

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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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