Question

Calcule o valor da integral ∫10(3x2+x-5)dx.

-2/5

2/5

-7/2

3

7/2

Answer 1

Olá

$\displaystyle \mathsf{ \int\limits^1_0 {(3x^2+x-5)} \, dx }\\\\\\ \mathsf{ 3\int\limits^1_0 {x^2} \, dx ~+~ \int\limits^1_0 {x} \, dx ~-~5\int\limits^1_0 {} \, dx }\\\\\\\mathsf{3\cdot \frac{x^{2+1}}{2+1} ~+~ \frac{x^{1+1}}{1+1} ~-~5x}\\\\\\\mathsf{\diagup\!\!\!\!3\cdot \frac{x^{3}}{\diagup\!\!\!\!3} ~+~ \frac{x^{2}}{2} ~-~5x}\\\\\\\mathsf{\left.\left(x^3+ \frac{x^2}{2}-5x \mathrm{}\right)\right|_{0}^{1}}\\\\\\\mathsf{\left((1)^3+ \frac{1^2}{2}-5\cdot 1\right) ~-~\left(0^3+ \frac{0^2}{2} -5\cdot 0\right)}$

$\displaystyle \mathsf{\left(1+ \frac{1}{2}-5 \right) -0}\\\\\\\mathsf{ \frac{2+1-10}{2} }\\\\\\\boxed{\mathsf{- \frac{7}{2} }}$