-14 f x dx -4 and -24-3- f x - dx -7 then -12 f x dx -A- 5B- 8C- -2D- 3

The correct option is A 5∫_2^4[3 f(x)]dx=7 ⇒∫_2^4 3 dx ∫_2^4 f(x)dx=7 ⇒ 6 ∫_2^4 f(x)dx=7⇒∫_2^4f(x)dx= 1 ⇒∫_2^ 1f(x)dx+∫_ 1^4f(x)dx= 1 ⇒∫_2^ 1f(x)dx+4= 1 ⇒∫ ...

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Byju's Answer

Standard XII

Mathematics

Integration of Piecewise Continuous Functions

∫-14 f x dx =...

Question

If $\int_{- 1}^{4} f (x) d x = 4$ and $\int_{2}^{4} [3 - f (x)] d x = 7 t h e n \int_{- 1}^{2} f (x) d x =$

-2

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Solution

The correct option is C 5
$\int_{2}^{4} [3 - f (x)] d x = 7 \Rightarrow \int_{2}^{4} 3 d x - \int_{2}^{4} f (x) d x = 7 \Rightarrow 6 - \int_{2}^{4} f (x) d x = 7 \Rightarrow \int_{2}^{4} f (x) d x = - 1$
$\Rightarrow \int_{2}^{- 1} f (x) d x + \int_{- 1}^{4} f (x) d x = - 1 \Rightarrow \int_{2}^{- 1} f (x) d x + 4 = - 1 \Rightarrow \int_{2}^{- 1} f (x) d x = - 5$
$\Rightarrow \int_{- 1}^{4} f (x) d x = 5$

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Similar questions

Q. If

\int_{- 1}^{4} f (x) d x = 4

and

\int_{2}^{4} [3 - f (x)] d x = 7

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If ∫4−1f(x)dx=4 and ∫42[3−f(x)]dx=7 then ∫2−1f(x)dx=

The correct option is C 5∫42[3−f(x)]dx=7⇒∫423dx−∫42f(x)dx=7⇒6−∫42f(x)dx=7⇒∫42f(x)dx=−1 ⇒∫−12f(x)dx+∫4−1f(x)dx=−1⇒∫−12f(x)dx+4=−1⇒∫−12f(x)dx=−5 ⇒∫4−1f(x)dx=5

If $\int_{- 1}^{4} f (x) d x = 4$ and $\int_{2}^{4} [3 - f (x)] d x = 7 t h e n \int_{- 1}^{2} f (x) d x =$