Q25 of 45 Page 1

Evaluate:

OR


Evaluate:

Let, I =


⇒ I =


⇒ I = …(1)


Using the property of definite integral:


∴ I =


⇒ I = {∵ sin (π/2 – x) = cos x}


⇒ I = …(2)


Adding equation 1 and 2, we get –


2I =


Using algebra of integrals we have –


2I =


⇒ 2I =


∴ I = π/12


OR


Let, I =


⇒ I =


⇒ I =


Let, I1 = and I2 =


∴ I = 3I1 + I2 …(1)


First, we will calculate I1 and I2 and then add both to get the answer.


Calculation of I1 :


Let x2 -9x + 20 = u


⇒ du = (2x - 9)dx


⇒ (2x - 9)dx = du


∴ I1 =


∴ I1 = + C1


∴ I1 = ...(2)


Calculation of I2 :


I2 =


⇒ I2 =


⇒ I2 =



Use the formula:


∴ I2 = …(3)


∴ From equation 1, 2 and 3 we have –


I = 3() +


∴ I =


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