$int_{0}^{3}-4x^{3}+5 dx$

$int_{0}^{3}-4x^{3}+5 dx$

$int_{0}^{3}-4x^{3}+5 dx$

Answer

Explanation:

Step1: Apply integral rules

$\int_{0}^{3}(-4x^{3}+5)dx=\int_{0}^{3}-4x^{3}dx+\int_{0}^{3}5dx$

Step2: Integrate each term

For $\int - 4x^{3}dx=-4\times\frac{x^{4}}{4}=-x^{4}+C_1$, and $\int5dx = 5x + C_2$. Then $\int_{0}^{3}-4x^{3}dx+\int_{0}^{3}5dx=\left[-x^{4}\right]{0}^{3}+\left[5x\right]{0}^{3}$

Step3: Evaluate definite - integrals

$\left[-x^{4}\right]{0}^{3}+\left[5x\right]{0}^{3}=(-3^{4}-(-0^{4}))+(5\times3 - 5\times0)=(-81 - 0)+(15 - 0)$

Step4: Calculate the result

$(-81)+15=-66$

Answer:

$-66$