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Definite Integration by properties - P4
Ex 7.10, 2
Ex 7.10, 3 Important You are here
Example 32 Important
Ex 7.10, 4
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, 3 By using the properties of definite integrals, evaluate the integrals : ∫_0^(𝜋/2)▒(sin^(3/2)𝑥 𝑑𝑥)/(sin^(3/2)𝑥 + cos^(3/2)𝑥 ) Let I=∫_0^(𝜋/2)▒〖(sin^(3/2) 𝑥)/(sin^(3/2) 𝑥 + cos^(3/2)𝑥 ) 𝑑𝑥〗 I= ∫_0^(𝜋/2)▒〖(sin^(3/2) (𝜋/2 − 𝑥))/(sin^(3/2) (𝜋/2 − 𝑥) + cos^(3/2) (𝜋/2 − 𝑥) ) 𝑑𝑥〗 ∴ I= ∫_0^(𝜋/2)▒〖cos^(3/2)𝑥/(cos^(3/2)𝑥 + sin^(3/2)𝑥 ) 𝑑𝑥〗 Adding (1) and (2) i.e. (1) + (2) I+I= sin^(3/2)𝑥/(sin^(3/2)𝑥 + cos^(3/2)𝑥 ) 𝑑𝑥+∫_0^(𝜋/2)▒〖cos^(3/2)𝑥/(cos^(3/2)𝑥 + sin^(3/2)𝑥 ) 𝑑𝑥〗 2I=∫_0^(𝜋/2)▒〖[(sin^(3/2)𝑥 + cos^(3/2)𝑥)/(sin^(3/2)𝑥 + cos^(3/2)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