it is given that \n int_{0}^{6} f(x) dx = 20 \text{ and } int_{3}^{6} f(x) dx = - 10 \nfind the value of…

it is given that \n int_{0}^{6} f(x) dx = 20 \text{ and } int_{3}^{6} f(x) dx = - 10 \nfind the value of (int_{0}^{3} f(x) dx)\ncircle your answer.\n-30, -10, 10, 30 1 mark

it is given that \n int_{0}^{6} f(x) dx = 20 \text{ and } int_{3}^{6} f(x) dx = - 10 \nfind the value of (int_{0}^{3} f(x) dx)\ncircle your answer.\n-30, -10, 10, 30 1 mark

Answer

Explanation:

Step1: Use integral property

We know that $\int_{0}^{6}f(x)dx=\int_{0}^{3}f(x)dx+\int_{3}^{6}f(x)dx$.

Step2: Rearrange to solve

$\int_{0}^{3}f(x)dx=\int_{0}^{6}f(x)dx-\int_{3}^{6}f(x)dx$.

Step3: Substitute values

Given $\int_{0}^{6}f(x)dx = 20$ and $\int_{3}^{6}f(x)dx=- 10$, then $\int_{0}^{3}f(x)dx=20-(-10)$.

Step4: Calculate result

$\int_{0}^{3}f(x)dx=20 + 10=30$.

Answer:

30