Chapter 7 Class 12 Integrals
Concept wise

Ex 7.10, 17 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by

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Ex 7.10, 17 By using the properties of definite integrals, evaluate the integrals : ∫_0^𝑎▒√𝑥/(√𝑥 + √(𝑎 − 𝑥)) 𝑑𝑥 Let I=∫_0^𝑎▒√𝑥/(√𝑥 + √(𝑎 − 𝑥)) 𝑑𝑥 ∴ I=∫_0^𝑎▒〖√(𝑎 − 𝑥)/(√(𝑎 − 𝑥) +√(𝑎 − (𝑎 − 𝑥) )) 𝑑𝑥〗 I= ∫_0^𝑎▒〖√(𝑎 − 𝑥)/(√(𝑎 − 𝑥) + √(𝑎 − 𝑎 + 𝑥)) 𝑑𝑥〗 I=∫_0^𝑎▒〖√(𝑎 − 𝑥)/(√(𝑎 − 𝑥) + √𝑥) 𝑑𝑥〗 Adding (1) and (2) i.e (1) + (2) I + I = ∫_0^𝑎▒〖√𝑥/(√𝑥 +√(𝑎 − 𝑥)) 𝑑𝑥〗+∫_0^𝑎▒〖√(𝑎 − 𝑥)/(√(𝑎− 𝑥) + √( 𝑥)) 𝑑𝑥〗 2I = ∫_0^𝑎▒〖(√𝑥 + √(𝑎 − 𝑥))/(√𝑥 + √(𝑎 − 𝑥)) 𝑑𝑥〗 2I =∫_0^𝑎▒〖1.𝑑𝑥〗 2I = [𝑥]_0^𝑎 2I = [𝑎−0] 𝐈 =𝒂/𝟐

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo