Here, we show you a step-by-step solved example of definite integrals. This solution was automatically generated by our smart calculator:
Expand the integral $\int_{0}^{2}\left(x^4+2x^2-5\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately
Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $4$
Evaluate the definite integral
Simplify the expression
The integral $\int_{0}^{2} x^4dx$ results in: $\frac{32}{5}$
The integral of a constant times a function is equal to the constant multiplied by the integral of the function
Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $2$
Evaluate the definite integral
Simplify the expression
The integral $\int_{0}^{2}2x^2dx$ results in: $\frac{16}{3}$
The integral of a constant is equal to the constant times the integral's variable
Evaluate the definite integral
Simplify the expression
The integral $\int_{0}^{2}-5dx$ results in: $-10$
Gather the results of all integrals
Simplify the addition $\frac{32}{5}+\frac{16}{3}-10$
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