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Definite Integration by properties - P4
Ex 7.10, 2
Ex 7.10, 3 Important
Example 32 Important
Ex 7.10, 4 You are here
Ex 7.10, 15
Ex 7.10, 17
Ex 7.10, 21 (MCQ) Important
Ex 7.10, 19
Ex 7.10, 12 Important
Ex 7.10, 9
Ex 7.10,7 Important
Example 30
Question 4 (MCQ) Important Deleted for CBSE Board 2024 Exams
Ex 7.10, 10 Important
Ex 7.10,8 Important
Example 34 Important
Ex 7.10, 16 Important
Question 2 Important Deleted for CBSE Board 2024 Exams
Example 42 Important
Definite Integration by properties - P4
Last updated at June 13, 2023 by Teachoo
Ex 7.10, 4 By using the properties of definite integrals, evaluate the integrals : ∫_0^(𝜋/2)▒(cos^5𝑥 𝑑𝑥)/(sin^5𝑥 + cos^5𝑥 ) Let I=∫_0^(𝜋/2)▒〖cos^5𝑥/(sin^5𝑥 + cos^5𝑥 ) 𝑑𝑥〗 I= ∫_0^(𝜋/2)▒〖(cos^5 (𝜋/2 − 𝑥))/(〖𝑠𝑖𝑛〗^5 (𝜋/2 − 𝑥) + 〖𝑐𝑜𝑠〗^5 (𝜋/2 − 𝑥) ) 𝑑𝑥〗 ∴ I = ∫_0^(𝜋/2)▒〖 sin^5𝑥/(cos^5𝑥 + sin^5𝑥 ) 𝑑𝑥〗 Adding (1) and (2) i.e. (1) + (2) I+I=(〖𝑐𝑜𝑠〗^5 𝑥)/(〖𝑠𝑖𝑛〗^5 𝑥 + 〖𝑐𝑜𝑠〗^5 𝑥) 𝑑𝑥+∫_0^(𝜋/2)▒〖sin^5𝑥/(cos^5𝑥 + sin^5𝑥 ) 𝑑𝑥〗 2I=∫_0^(𝜋/2)▒〖[(〖𝑐𝑜𝑠〗^5 𝑥 + 〖𝑠𝑖𝑛〗^5 𝑥)/(〖𝑐𝑜𝑠〗^5 𝑥 + 〖𝑠𝑖𝑛〗^5 𝑥)] 𝑑𝑥〗 2I= ∫_0^(𝜋/2)▒〖 𝑑𝑥〗 I=1/2 ∫_0^(𝜋/2)▒〖 𝑑𝑥〗 I=1/2 [𝑥]_0^(𝜋/2) I=1/2 [𝜋/2−0] 𝑰=𝝅/𝟒