Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2010MathematicsDefinite Integration

₀¹ x(1-x)^ 3 / 2 d x is

Options

  1. A- 2 35
  2. B4 35
  3. C24 35
  4. D- 8 35

Correct answer

B. 4 35

Step-by-step solution

₀¹ x(1-x)^ 3 / 2 d x= ₀¹ x ^ (2-1) (1- x )^ 5 / 2-1 dx = B (2,5 / 2) array l B ( m , n )= ₀¹ x ^ m -1 (1- x )^ n -1 dx B ( m , n )= m n ( m + n ) array .= 2 5 / 2 (2+5 / 2) = 1 3 / 2 1 / 2 1 / 2 9 / 2 ( 1 / 2= )= 3 / 4 7 / 2 5 / 2 3 / 2 1 / 2 = 4 35

Practice Definite Integration on Quantrex Academy →

More from Definite Integration

₀^1 2 x+5 x^2+3 x+2 ~d x= 2025₀^1 x^ 5 / 2 (1-x)^ 3 / 2 ~d x= 2025_ n [ 1 n^2 ^2 1 n^2 + 2 n^2 ^2 4 n^2 + 3 n^2 ^2 9 n^2 + + 1 n^2 ^2 1 ]= 2025₀^1 x Sin ⁻¹ x d x= 2025_ - 2 ^ 2 (x-[x]) d x= 2025₀^2 x^2(2-x)^5 d x= 2025If f(x)= Max x^3-4, x^4-4 , and g(x)= Min x^2, x^3 , then _ -1 ^1(f(x)-g(x)) d x= 2025_ n 2 n [ 2 n + 2 2 n + 3 2 n + + 2 ]= 2025 Full Definite Integration list All KCET PYQs