Ex 7.10, 17 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Ex 7.10
Ex 7.10, 1
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Chapter 7 Class 12 Integrals
Serial order wise
Transcript
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
