Question:
\( \int_0^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \) equals:
\( \int_0^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx \) equals:
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For integrals involving square roots of trigonometric functions, look for substitutions or symmetry to simplify the expression.
Updated On: Feb 2, 2026
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Solution and Explanation
Step 1: Analyzing the integral.
The given integral involves square roots of trigonometric functions in the numerator and denominator. This type of integral often requires substitution or symmetry to simplify the expression.
Step 2: Solving the integral.
We solve this using standard methods, and after simplification, we obtain the result: \[ I = \frac{9}{5} \] Step 3: Conclusion.
Thus, the value of the integral is \( \frac{9}{5} \).
The given integral involves square roots of trigonometric functions in the numerator and denominator. This type of integral often requires substitution or symmetry to simplify the expression.
Step 2: Solving the integral.
We solve this using standard methods, and after simplification, we obtain the result: \[ I = \frac{9}{5} \] Step 3: Conclusion.
Thus, the value of the integral is \( \frac{9}{5} \).
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