section 14: ftoc & antidifferentiation score: 10/11 answered: 7/8 question 8 suppose ∫₄¹⁰ f(x) dx = 5 and…
section 14: ftoc & antidifferentiation score: 10/11 answered: 7/8 question 8 suppose ∫₄¹⁰ f(x) dx = 5 and ∫₁₀¹¹ f(x) dx = 9. then ∫₄¹¹ f(x) dx = question help: video written example
Answer
Explanation:
Step1: Use integral property
By the property of definite - integrals $\int_{a}^{c}f(x)dx=\int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx$ where $a < b < c$. Here, $a = 4$, $b = 10$, $c = 11$. So $\int_{4}^{11}f(x)dx=\int_{4}^{10}f(x)dx+\int_{10}^{11}f(x)dx$.
Step2: Substitute given values
We know that $\int_{4}^{10}f(x)dx = 5$ and $\int_{10}^{11}f(x)dx = 9$. Substituting these values into the above formula, we get $\int_{4}^{11}f(x)dx=5 + 9$.
Answer:
14