Question

Integrate: $(7x^3 + 4x^2) dx$

• A. $(7x^4/4) + (4x^2/4) + C$
• B. $(7x^4/4) + (4x^2/5) + C$
• C. $(7x^4/4) + (4x^3/3) + C$
• D. $7x^4 + (4x^2/2) + C$

Answer 1

Answer: (C)

$(7x^4/4) + (4x^3/3) + C$

Answer 2

To integrate $(7x^3 + 4x^2) dx$, apply the linearity of integration and the power rule $\int x^n dx = \frac{x^{n+1}}{n+1} + C$.

For the first term, $\int 7x^3 dx = 7 \frac{x^{3+1}}{3+1} = \frac{7x^4}{4}$.

For the second term, $\int 4x^2 dx = 4 \frac{x^{2+1}}{2+1} = \frac{4x^3}{3}$.

Combining these, the integral is $\frac{7x^4}{4} + \frac{4x^3}{3} + C$.