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Integration by parts
Ex 7.6, 3 You are here
Ex 7.6, 23 (MCQ)
Example 17
Ex 7.6, 1
Ex 7.6, 2 Important
Ex 7.6, 12
Example 21 Important
Ex 7.6, 21
Ex 7.6, 5 Important
Ex 7.6, 4
Ex 7.6, 6
Ex 7.6, 15
Example 18 Important
Ex 7.6, 14 Important
Ex 7.6, 7 Important
Ex 7.6, 9
Ex 7.6, 8
Ex 7.6, 11
Example 20 Important
Ex 7.6, 13 Important
Ex 7.6, 22 Important
Ex 7.6, 10 Important
Example 40 Important
Integration by parts
Last updated at Dec. 20, 2019 by Teachoo
Ex 7.6, 3 Integrate the function π₯^2 ππ₯ β«1βγπ₯^2 π^π₯ ππ₯γ = π₯^2 β«1βγππ₯ ππ₯γββ«1β(π(π₯^2 )/ππ₯ β«1βγππ₯ ππ₯γ) ππ₯ = π₯^2. ππ₯ ββ«1βγ2π₯ . ππ₯γ ππ₯ = π₯^2. ππ₯ β2β«1βγπ . ππγ π π Now we know that β«1βγπ(π₯) πβ‘(π₯) γ ππ₯=π(π₯) β«1βπ(π₯) ππ₯ββ«1β(πβ²(π₯)β«1βπ(π₯) ππ₯) ππ₯ Putting f(x) = x2 and g(x) = ex β¦(1) Solving I1 β«1βγπ₯ π^π₯ ππ₯γ = π₯β«1βππ₯ ππ₯ββ«1β(ππ₯/ππ₯ β«1βπ^π₯ ππ₯) ππ₯ = π₯ππ₯ ββ«1βππ₯ ππ₯ = π₯ππ₯ βππ₯ Now we know that β«1βγπ(π₯) πβ‘(π₯) γ ππ₯=π(π₯) β«1βπ(π₯) ππ₯ββ«1β(πβ²(π₯)β«1βπ(π₯) ππ₯) ππ₯ Putting f(x) = x and g(x) = ex Putting value of I1 in our equation β΄ β«1βγπ₯^2 ππ₯" " γ ππ₯" = " π₯^2. ππ₯ β2β«1βγπ . ππγ π π =π₯^2. ππ₯ β2(πππβπ^π )+πΆ =π₯^2. ππ₯ β2π₯ππ₯+γ2πγ^π₯+πΆ =ππ (π^πβππ+π)+πͺ