Question

\[ \int_{0}^{10}\frac{x^{10}}{(10-x)^{10}+x^{10}}\,dx \] is equal to

• A. \(10\)
• B. \(5\)
• C. \(2\)
• D. \(\dfrac{1}{2}\)

Hint:

For symmetric limits, try \(x \to a-x\).

Answer 1

The Correct Option is B

Step 1: Use property: \[ \int_0^a f(x)\,dx=\int_0^a f(a-x)\,dx \]
Step 2: Adding both integrals: \[ 2I=\int_0^{10}1\,dx=10 \]
Step 3: \[ I=5 \]