Question

Use the table of integrals to evaluate the integral. 2 0 5x3 4x2 − x4?

Answer 1

To evaluate the integral ∫(5x^3 - 4x^2 - x^4) dx, we can use the table of integrals. The final result is (1/4)x^4 - (4/3)x^3 - (1/5)x^5 + C.

Step-by-step explanation:

To evaluate the integral ∫(5x^3 - 4x^2 - x^4) dx, we can use the table of integrals. From the table, we can find that ∫x^n dx = (1/(n+1))x^(n+1) + C, where n is any real number and C is the constant of integration.

1. Simplify the integral to ∫(5x^3 - 4x^2 - x^4) dx.
2. Use the table of integrals to apply the formula ∫x^n dx = (1/(n+1))x^(n+1) + C for each term.
3. Apply the formula to each term, so the integral becomes (1/4)x^4 - (4/3)x^3 - (1/5)x^5 + C.

The final result is ∫(5x^3 - 4x^2 - x^4) dx = (1/4)x^4 - (4/3)x^3 - (1/5)x^5 + C.