Question

The value of the integral intₐᵇ frac√(x)dx√(x)+√(a+b-x) is:

• A. \(\pi\)
• B. \(\dfrac{1}{2}(b-a)\)
• C. \(\dfrac{\pi}{2}\)
• D. b-a

Hint:

Use symmetry property: I=intₐᵇ f(x)dx=intₐᵇ f(a+b-x)dx.

Answer 1

The Correct Option is B

Step 1: Replace x→ a+b-x and add both forms.
Step 2: I+I=intₐᵇ dx=b-a ⟹ I=(b-a)/(2)