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  • Please Solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.3 Question 1 Subquestion (iii) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 19 Definite Integrals Exercise 19.3 Question 1 Subquestion (iii) Maths Textbook Solution.

Answers (1)

Answer:   62

Hint: Break the range of integration and then solve the integration.

Given:   \int_{1}^{4} f(x) d x \text { where } f(x)

                             =\left\{\begin{array}{ll} 7 x+3, & \text { if } 1 \leq x \leq 3 \\ 8 x, & \text { if } 3 \leq x \leq 4 \end{array}\right\}

Solution:

                 \int_{1}^{4} f(x) d x

                 \begin{aligned} &=\int_{1}^{3} f(x) d x+\int_{3}^{4} f(x) d x \\ & \end{aligned}                                     

                 =\int_{1}^{3}(7 x+3) d x+\int_{3}^{4} 8 x d x                                      \quad\left[\because \int x^{n} d x=\frac{x^{n+1}}{n+1}+c\right]

                 \begin{aligned} &=\left[\frac{7 x^{2}}{2}+3 x\right]_{1}^{3}+\left[\frac{8 x^{2}}{2}\right]_{3}^{4} \\ & \end{aligned}

                 =\left[7 \frac{(9-1)}{2}+3(3-1)\right]+4(16-9) \\

                 =7(4)+3(2)+4(7) \\

                 =28+6+28 \\

                 =62

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