If $\int_{- 1}^{4}{f(x)dx = 4}$ and $\int_{2}^{4}{\left\{ 3 - f(x) \right\} dx = 7}$, then the value of $\int_{- 1}^{2}{f(x)}dx$ is

Question

Dr. Abubacker · Accepted Answer

(d)
Since, $\int_{2}^{4}{\{ 3 - f(x)}\} dx = 7$
$\Rightarrow \ 3\lbrack xbrack_{2}^{4} - \int_{2}^{4}{f(x)}dx = 7$
$\Rightarrow \ \int_{2}^{4}{f(x)}dx = 6 - 7 = - 1$
$	herefore\ \int_{- 1}^{2}{f(x)}dx = \int_{- 1}^{4}{f(x)}dx - \int_{2}^{4}{f(x)}dx$
$= 4 - ( - 1) = 5$

Q. If $\int_{- 1}^{4}{f(x)dx = 4}$ and $\int_{2}^{4}{\left\{ 3 - f(x) \right\} dx = 7}$, then the value of $\int_{- 1}^{2}{f(x)}dx$ is

Explanation

Reviewed by Dr. Abubacker

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