Ex 7.8, 15 - Chapter 7 Class 12 Integrals (Important Question)

Last updated at Dec. 16, 2024 by Teachoo

Ex 7.8, 15 - Direct Integrate x ex^2 dx from 0 to 1 - Teachoo - Ex 7.8

part 2 - Ex 7.8, 15 - Ex 7.8 - Serial order wise - Chapter 7 Class 12 Integrals

part 3 - Ex 7.8, 15 - Ex 7.8 - Serial order wise - Chapter 7 Class 12 Integrals

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Transcript

Ex 7.8, 15 ∫_0^1▒〖𝑥𝑒^(𝑥^2 ) 〗 𝑑𝑥 Step 1 :- Let F(𝑥)=∫1▒〖𝑥𝑒^(𝑥^2 ) 𝑑𝑥〗 Let 𝑥^2=𝑡 Differentiating w.r.t. 𝑥 2𝑥=𝑑𝑡/𝑑𝑥 𝑑𝑥=𝑑𝑡/2𝑥 Therefore, ∫1▒〖𝑥 𝑒^(𝑥^2 ) 𝑑𝑥=∫1▒〖𝑥 𝑒^𝑡 𝑑𝑡/2𝑥〗〗 =1/2 ∫1▒〖𝑒^𝑡 𝑑𝑡〗 =1/2 𝑒^𝑡 Putting 𝑡=𝑥^2 =1/2 𝑒^(𝑥^2 ) Hence, F(𝑥)=1/2 𝑒^(𝑥^2 ) Step 2 :- ∫_0^1▒〖𝑥𝑒^(𝑥^2 ) 𝑑𝑥〗=𝐹(1)−𝐹(0) =1/2 𝑒^(1^2 )−1/2 𝑒^(0^2 ) =1/2 𝑒^1−1/2 𝑒^0 =𝟏/𝟐 (𝒆−𝟏)

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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

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