Evaluate the Integral

Problem

(∫_^)(√(,y)*d(y))

Solution

1. Rewrite the radical expression using a fractional exponent to make it easier to apply the power rule for integration.

(∫_^)(y(1/2)*d(y))

2. Apply the power rule for integration, which states that (∫_^)(yn*d(y))=(y(n+1))/(n+1)+C for n≠−1

(y(1/2+1))/(1/2+1)+C

3. Simplify the exponent and the denominator by performing the addition.

(y(3/2))/(3/2)+C

4. Multiply by the reciprocal of the denominator to simplify the fraction.

2/3*y(3/2)+C

Final Answer

(∫_^)(√(,y)*d(y))=2/3*y(3/2)+C

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