AP EAMCET202318 May 2023Morning ShiftMathematicsDefinite IntegrationActual
₀^ x ^3 x ^2 x d x=
Options
- A2 15
- B4 15
- C30
- D2 5
Correct answer
A. 2 15
Step-by-step solution
Let ₀^ x ^3 x ^2 x d x=I ...(i) I= ₀^ ( -x) ^3( -x) ^2( -x) d xI= ₀^ ( -x) ^3(x) ^2 x d x ...(ii) Equation (i) + (ii) 2 I= ₀^ ^3 x ^2 x d x= ₀^ (1- ^2 x ) ^2 x x d x Let x=t - x d x=d t 2 I = ₁⁻¹ (1- t ^2 ) t ^2(- dt )= _ -1 ^1 ( t ^2- t ^4 ) dt = [ t^3 3 - t^5 5 ]_ -1 ^1 2 I= 4 15 I= 2 15