If $\int_{-1}^4f(x) dx = 4$ and $\int_2^

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Definite Integration

Question:

If $\int_{-1}^4f(x) dx = 4$ and $\int_2^4(3-f(x)) dx = 7$, the value of $\int_2^{-1}f(x)dx$ is

Options:

-3

-5

none of these

Correct Answer:

-5

Explanation:

$∵\int_{-1}^4f(x) dx = 4$ and $\int_2^4(3-f(x)) dx = 7$

or $\int_4^{-1}f(x)dx=-4$ and $6-\int_2^4f(x)dx=7$

$∴\int_4^{-1}f(x)dx=-4,\int_2^4f(x)dx=-1$

$\int_2^{-1}f(x)dx=\int_2^4f(x)dx+\int_4^{-1}f(x)dx=-1-4=-5$