Question

1 (a) Evaluate the integral sz? dx. (32-7) 5 2 7 (b)if s f(x)dx = 3 and 5 f(x)dt = 4, find S f(x)dr. 5

Answer 1

a) This is a standar type of integral wherein you have to substitute 3x-7 into one variable t and carry out the integration as usual with the limits changed.

The image below has the solution

dre (3 74 - 7 3a -I-2 dn 3 put 3x - 7-t dt 3 da de = Idt bir change into: 3(32-7 = 2 3 (4) -7 25 So, the integral changes to t at 3. -d+1 - t ti - 2+1 ilm ale IT

b)

This question is based on splitting of limits and the limit exchange rule. Check the image for the solution

b) Given si f(x) dx = 3 3 f(x) dx = 4 2 7 7 We need to find l flas de A theorem in integration bays b 6 d fond du fluidat faida a I fronder Sacolo. Posta e garantee 0 2 also; "f feesdae = -) sos de Lan applying (i) in (1) - 4 = 3 & s tendre har i so J fonda za is given froida = - 7

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