Evaluate the Integral integral of 10x with respect to x

Problem

(∫_^)(10*x*d(x))

Solution

1. Identify the constant factor in the integrand. Since 10 is a constant, it can be moved outside the integral.

(∫_^)(10*x*d(x))=10*(∫_^)(x*d(x))

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

10*(∫_^)(x1*d(x))=10⋅(x(1+1))/(1+1)

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

10⋅(x2)/2

4. Reduce the fraction by dividing 10 by 2

5*x2

5. Add the constant of integration C to represent the family of antiderivatives.

5*x2+C

Final Answer

(∫_^)(10*x*d(x))=5*x2+C

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