If -14 fx dx - 4 and -24 3 - fxdx - 7- then which of the following is-are true-

We have ∫_2^4 (3 f(x))dx =7 ⇒ 6 ∫_2^4 f(x) dx=7 ⇒∫_2^4 f(x)dx = 1 Now, nbsp; ∫_ 1^4 f(x)dx =4 ⇒ 4= ∫_ 1^2 f(x)dx + ∫_2^4 f(x)dx ⇒ nbsp; ∫_ 1^2 f(x)dx ...

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Byju's Answer

Standard XII

Mathematics

Change of Variables

If ∫-14 fx dx...

Question

If $4 \int - 1 f (x) d x = 4$ and $4 \int 2 (3 - f (x)) d x = 7$ , then which of the following is/are true:

4 \int 2 f (x) d x = - 1

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4 \int 2 f (x) d x = 1

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2 \int - 1 f (x) d x = 5

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2 \int - 1 f (x) d x = - 5

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Solution

The correct option is C $2 \int - 1 f (x) d x = 5$
We have
$4 \int 2 (3 - f (x)) d x = 7 \Rightarrow 6 - 4 \int 2 f (x) d x = 7 \Rightarrow 4 \int 2 f (x) d x = - 1$
Now,
$4 \int - 1 f (x) d x = 4 \Rightarrow 4 = 2 \int - 1 f (x) d x + 4 \int 2 f (x) d x \Rightarrow 2 \int - 1 f (x) d x - 1 = 4 \Rightarrow 2 \int - 1 f (x) d x = 5$

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Change of Variables

Standard XII Mathematics

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If 4∫−1f(x)dx=4 and 4∫2(3−f(x))dx=7, then which of the following is/are true:

The correct option is C 2∫−1f(x)dx=5We have 4∫2(3−f(x))dx=7⇒6−4∫2f(x) dx=7⇒4∫2f(x)dx=−1 Now, 4∫−1f(x)dx=4⇒4=2∫−1f(x)dx+4∫2f(x)dx⇒2∫−1f(x)dx−1=4⇒2∫−1f(x)dx=5

If $4 \int - 1 f (x) d x = 4$ and $4 \int 2 (3 - f (x)) d x = 7$ , then which of the following is/are true: