Evaluate the Integral integral of 3t with respect to t

Problem

(∫_^)(3*t*d(t))

Solution

1. Identify the constant and the variable of integration. The constant is 3 and the variable is t

2. Apply the constant multiple rule for integration by moving the constant 3 outside the integral.

(∫_^)(3*t*d(t))=3*(∫_^)(t*d(t))

3. Apply the power rule for integration, which states that (∫_^)(tn*d(t))=(t(n+1))/(n+1) for n≠−1 Here, n=1

3*(∫_^)(t1*d(t))=3⋅(t(1+1))/(1+1)

4. Simplify the expression and add the constant of integration C

3⋅(t2)/2+C=3/2*t2+C

Final Answer

(∫_^)(3*t*d(t))=3/2*t2+C

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