Evaluate the Integral integral of 14x with respect to x

Problem

(∫_^)(14*x*d(x))

Solution

1. Identify the constant factor in the integrand.

2. Apply the constant multiple rule for integration by moving the 14 outside the integral.

(∫_^)(14*x*d(x))=14*(∫_^)(x*d(x))

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

14*(∫_^)(x1*d(x))=14⋅(x(1+1))/(1+1)

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

14⋅(x2)/2

5. Divide the constant 14 by 2 and add the constant of integration C

7*x2+C

Final Answer

(∫_^)(14*x*d(x))=7*x2+C

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