If $\int_{0}^{6} f(x) d x=15$ and $\int_{0}^{4} f(x) d x=6$ , find $\int_{4}^{6} f(x) d x$ .
A) 6
B) 21
C) 15
D) 9
E) $-15$

Question

Quizplus · Accepted Answer

The integral from 0 to 6 can be split into two parts: from 0 to 4 and from 4 to 6. Therefore, $\int_{0}^{6} f(x) dx = \int_{0}^{4} f(x) dx + \int_{4}^{6} f(x) dx$. Given $\int_{0}^{6} f(x) dx = 15$ and $\int_{0}^{4} f(x) dx = 6$, we have $15 = 6 + \int_{4}^{6} f(x) dx$. Solving for $\int_{4}^{6} f(x) dx$, we get $\int_{4}^{6} f(x) dx = 15 - 6 = 9$.

If ∫06f(x)dx=15\int_{0}^{6} f(x) d x=15∫06​f(x)dx=15 And ∫04f(x)dx=6\int_{0}^{4} f(x) d x=6∫04​f(x)dx=6 , Find ∫46f(x)dx\int_{4}^{6} f(x) d x∫46​f(x)dx

If $\int_{0}^{6} f(x) d x=15$ And $\int_{0}^{4} f(x) d x=6$ , Find $\int_{4}^{6} f(x) d x$