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Manipal MET2012MathematicsDefinite Integration

The value of ₂^3 x 5-x + x d x is

Options

  1. A1
  2. B1 / 2
  3. C2
  4. DNone of these

Correct answer

B. 1 / 2

Step-by-step solution

array llrl Let & & I= ₂^3 x 5-x + x d x ....(i) & & I= ₂^3 5-x x + 5-x d x ....(ii) array On adding Eqs. (i) and (ii), we get aligned 2 I & = ₂^ 3 x + 5-x x + 5-x d x & = ₂^3 1 d x=3-2=1 I & = 1 2 aligned

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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 Manipal MET PYQs