Evaluate the Integral integral of -10x^4 with respect to x

Problem

(∫_^)(−10*x4*d(x))

Solution

1. Identify the constant and the power of x in the integrand.

2. Apply the constant multiple rule by moving the constant −10 outside the integral.

(∫_^)(−10*x4*d(x))=−10*(∫_^)(x4*d(x))

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

−10*(∫_^)(x4*d(x))=−10⋅(x(4+1))/(4+1)+C

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

−10⋅(x5)/5+C

5. Divide the constant coefficients to find the final simplified form.

−2*x5+C

Final Answer

(∫_^)(−10*x4*d(x))=−2*x5+C

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