Question

if $int_{1}^{7}f(x)dx = 14$ and $int_{5}^{7}f(x)dx = 5.7$, find $int_{1}^{5}f(x)dx$.

Explanation:

Step1: Use integral property

We know that $\int_{a}^{c}f(x)dx=\int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx$ for $a < b < c$. Here, $\int_{1}^{7}f(x)dx=\int_{1}^{5}f(x)dx+\int_{5}^{7}f(x)dx$.

Step2: Rearrange to solve

Let $A = \int_{1}^{5}f(x)dx$, $B=\int_{5}^{7}f(x)dx$ and $C=\int_{1}^{7}f(x)dx$. Then $C = A + B$. We want to find $A$, so $A=C - B$. Given $C = 14$ and $B = 5.7$, we have $A=14 - 5.7$.

Answer:

$8.3$