What is the value of ∫_0^(pi/2) sin^3x cos x dx?
∫_0^(pi/2) sin^3x cos x dx का मान क्या है?
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Correct Answer
C. 1 / 4
ExplanationStep 1: put u=sin x, so du=cos x dx. Step 2: limits become 0 to 1 and the integral is ∫_0^1 u^3du = 1/4 = 1/4. Step 3: tip: for a sine power with a cos factor, u=sin x is fastest.
Step 1: u=sin x रखें, इसलिए du=cos x dx। Step 2: limits 0 से 1 हो जाती हैं और integral ∫_0^1 u^3du = 1/4 = 1/4। Step 3: tip: sin power with cos factor में u=sin x fastest है।