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  • Explain solution RD Sharma class 12 Chapter 19 Definite Integrals Exercise Revision Exercise question 67

Explain solution RD Sharma class 12 Chapter 19 Definite Integrals Exercise Revision Exercise question 67

Answers (1)

Answer:  \frac{62}{3}

Hint: To solve the given statement we have to integrate them individually.

Given: \int_{1}^{3}\left(x^{2}+3 x\right) d x

Solution:

\begin{aligned} &\int_{1}^{3}\left(x^{2}+3 x\right) d x \\ &\int_{1}^{3}\left(x^{2}+3 x\right) d x \\ &=\int_{1}^{3} x^{2} d x+\int_{1}^{3} 3 x d x \end{aligned}

\begin{aligned} &=\left[\frac{x^{3}}{3}\right]_{1}^{3}+3\left[\frac{x^{2}}{2}\right]_{1}^{3} \\ &=\frac{27-1}{3}+3\left[\frac{9-1}{2}\right] \\ &=\frac{26}{3}+\frac{24}{2} \\ &=\frac{26+36}{3} \\ &=\frac{62}{3} \end{aligned}

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