2 it is given that ∫₀⁶ f(x) dx = 20 and ∫₃⁶ f(x) dx = -10 find the value of ∫₀³ f(x) dx circle your answer…
2 it is given that ∫₀⁶ f(x) dx = 20 and ∫₃⁶ f(x) dx = -10 find the value of ∫₀³ 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
$\int_{0}^{3}f(x)dx=\int_{0}^{6}f(x)dx - \int_{3}^{6}f(x)dx$.
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
$\int_{0}^{3}f(x)dx = 30$.
Answer:
30