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

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

Answers (1)

Answer:  37

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

Given:

                \int_{1}^{4} f(x) d x \text { where } f(x)=\left\{\begin{array}{ll} 4 x+3, & \text { if } 1 \leq x \leq 2 \\ 3 x+5, & \text { if } 2 \leq x \leq 4 \end{array}\right\}

Solution:

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

Now break the limit =   \int_{1}^{2} f(x) d x+\int_{2}^{4} f(x) d x=\int_{1}^{2}(4 x+3) d x+\int_{2}^{4}(3 x+5) d x

                                                       =\left[\frac{4 x^{2}}{2}+3 x\right]_{1}^{2}+\left[\frac{3 x^{2}}{2}+5 x\right]_{2}^{4}                            \quad\left[\because \int x^{n} d x=\frac{x^{n+1}}{n+1}+c\right]

                                                       \begin{aligned} &=\left(2 x^{2}+3 x\right)_{1}^{2}+\left(\frac{3 x^{2}}{2}+5 x\right)_{2}^{4} \\ & \end{aligned}

                                                       =2(4-1)+3(2-1)+\frac{3}{2}(16-4)+5(4-2) \\

                                                       =6+3+18+10 \\

                                                       =37

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