Evaluate the following Integral:∫ f(x) dx, x ∈ [1, 4 ]where f(x) = {(7x +3, if 1≤ x ≤ 3), (8x, if 3 ≤ x ≤ 4)

Question

Evaluate the following Integral:

\(\int\limits_{1}^{4} \)f(x)dx, where f(x) = \( \begin{cases} 7\text x+3, & \quad \text{if } 1\leq\text x\leq3\\ 8\text x, & \quad \text{if } 3\leq\text x\leq4 \end{cases} \)

Answer 1

We have, \(\int\limits_{1}^{4} \)f(x)dx

= 34 + 28

Hence, 62