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Ex 7.10
Ex 7.10, 2
Ex 7.10, 3 Important
Ex 7.10, 4 You are here
Ex 7.10, 5 Important
Ex 7.10, 6
Ex 7.10,7 Important
Ex 7.10,8 Important
Ex 7.10, 9
Ex 7.10, 10 Important
Ex 7.10, 11 Important
Ex 7.10, 12 Important
Ex 7.10, 13
Ex 7.10, 14
Ex 7.10, 15
Ex 7.10, 16 Important
Ex 7.10, 17
Ex 7.10, 18 Important
Ex 7.10, 19
Ex 7.10, 20 (MCQ) Important
Ex 7.10, 21 (MCQ) Important
Last updated at May 29, 2023 by Teachoo
Ex 7.10, 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