Final Answer
$\frac{182}{3}$
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Step-by-step Solution
Problem to solve:
$\int_{2}^{4}\left(x^2+5x+6\right)dx$
Specify the solving method
1
Expand the integral $\int_{2}^{4}\left(x^2+5x+6\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately
$\int_{2}^{4} x^2dx+\int_{2}^{4}5xdx+\int_{2}^{4}6dx$
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$\int_{2}^{4} x^2dx+\int_{2}^{4}5xdx+\int_{2}^{4}6dx$
Learn how to solve problems step by step online. Integrate the function x^2+5x+6 from 2 to 4. Expand the integral \int_{2}^{4}\left(x^2+5x+6\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{2}^{4} x^2dx results in: \frac{56}{3}. The integral \int_{2}^{4}5xdx results in: 30. The integral \int_{2}^{4}6dx results in: 12.
Final Answer
$\frac{182}{3}$