Evaluate the following Integral: ∫f(x) dx, x ∈ [1, 4] where f(x)= {(4x +3, if 1 ≤ x ≤ 2), (3x + 5, if 2 ≤ x ≤ 4)

Question

Evaluate the following Integral:

\(\int\limits_{1}^{4} \)f(x) dx, where f(x)= \( \begin{cases} 4\text x+3, & \quad \text{if } 1\leq\text x\leq2\\ 3\text x+5, & \quad \text{if } 2\leq\text x\leq4 \end{cases} \)

Answer 1

We have, \(\int\limits_1^4\)f(x)dx

= [14 – 5 ] + [44 – 16]

= 9 + 28

= 37