2 it is given that $int_{0}^{6}f(x)dx = 20$ and $int_{3}^{6}f(x)dx=-10$. find the value of…
2 it is given that $int_{0}^{6}f(x)dx = 20$ and $int_{3}^{6}f(x)dx=-10$. find the value of $int_{0}^{3}f(x)dx$. circle your answer. 1 mark -30 -10 10 30
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
Let $I = \int_{0}^{3}f(x)dx$. Then $I=\int_{0}^{6}f(x)dx-\int_{3}^{6}f(x)dx$. Substitute $\int_{0}^{6}f(x)dx = 20$ and $\int_{3}^{6}f(x)dx=- 10$ into the equation: $I = 20-(-10)$.
Step3: Calculate result
$I=20 + 10=30$.
Answer:
30