# Ex 7.11, 4 - Chapter 7 Class 12 Integrals

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 7.11, 4 By using the properties of definite integrals, evaluate the integrals : 0 𝜋2 cos5𝑥 𝑑𝑥 sin5𝑥 + cos5𝑥 Let I= 0 𝜋2 cos5𝑥 sin5𝑥 + cos5𝑥 𝑑𝑥 I= 0 𝜋2 cos5 𝜋2 − 𝑥 𝑠𝑖𝑛5 𝜋2 − 𝑥 + 𝑐𝑜𝑠5 𝜋2 − 𝑥 𝑑𝑥 ∴ I = 0 𝜋2 sin5𝑥 cos5𝑥 + sin5𝑥 𝑑𝑥 Adding (1) and (2) i.e. (1) + (2) I+I= 𝑐𝑜𝑠5 𝑥 𝑠𝑖𝑛5 𝑥 + 𝑐𝑜𝑠5 𝑥 𝑑𝑥+ 0 𝜋2 sin5𝑥 cos5𝑥 + sin5𝑥𝑑𝑥 2I= 0 𝜋2 𝑐𝑜𝑠5 𝑥 + 𝑠𝑖𝑛5 𝑥 𝑐𝑜𝑠5 𝑥 + 𝑠𝑖𝑛5 𝑥 𝑑𝑥 2I= 0 𝜋2 𝑑𝑥 I= 12 0 𝜋2 𝑑𝑥 I= 12 𝑥0 𝜋2 I= 12 𝜋2−0 𝑰= 𝝅𝟒

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