Question

1. if $int_{1}^{5}f(x)dx = 12$ and $int_{4}^{5}f(x)dx = 3.6$, find $int_{1}^{4}f(x)dx$.

Explanation:

Step1: Use integral property

We know that $\int_{a}^{c}f(x)dx=\int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx$. So, $\int_{1}^{5}f(x)dx=\int_{1}^{4}f(x)dx+\int_{4}^{5}f(x)dx$.

Step2: Rearrange to solve

Let $I = \int_{1}^{4}f(x)dx$. Then $I=\int_{1}^{5}f(x)dx-\int_{4}^{5}f(x)dx$.
Substitute $\int_{1}^{5}f(x)dx = 12$ and $\int_{4}^{5}f(x)dx=3.6$ into the above - formula.
$I = 12 - 3.6$.

Answer:

$8.4$