Evaluate the Integral integral of 5ydy with respect to y

Problem

(∫_^)(5*y*d(y))

Solution

1. Identify the constant factor in the integrand. The constant 5 can be moved outside the integral.

(∫_^)(5*y*d(y))=5*(∫_^)(y*d(y))

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

5*(∫_^)(y1*d(y))=5⋅(y(1+1))/(1+1)+C

3. Simplify the expression by performing the arithmetic in the exponent and the denominator.

5⋅(y2)/2+C

4. Rewrite the final expression as a single fraction.

(5*y2)/2+C

Final Answer

(∫_^)(5*y*d(y))=(5*y2)/2+C

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