Evaluate int_(0)^(4)(9e^(0.5 x)-2x)dx and express the answer in simplest form. Answer:

Evaluate Definite Integral: Now we evaluate the definite integral from 0 to 4. $\int_{0}^{4}(9e^{0.5x}-2x)dx = [18e^{0.5x} - x^2]_{0}^{4}$ We calculate the value of the antiderivative at the upper limit of integration (x = 4): $18e^{0.5 \cdot 4} - 4^2 = 18e^{2} - 16$Calculate Upper Limit: Next, we calculate the value of the antiderivative at the lower limit of integration (x = 0): $18e^{0.5 \cdot 0} - 0^2 = 18e^{0} - 0 = 18 \cdot 1 - 0 = 18$Calculate Lower Limit: We subtract the value of the antiderivative at the lower limit from the value at the upper limit to find the definite integral: $[18e^{2} - 16] - [18]$ $18e^{2} - 16 - 18$ $18e^{2} - 34$

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Evaluate
int_(0)^(4)(9e^(0.5 x)-2x)dx and express the answer in simplest form.
Answer:

Evaluate $\int_{0}^{4}\left(9 e^{0.5 x}-2 x\right) d x$ and express the answer in simplest form. $\newline$ Answer:

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Calculus

Evaluate definite integrals using the chain rule

Full solution

Q. Evaluate

\int_{0}^{4}\left(9 e^{0.5 x}-2 x\right) d x

and express the answer in simplest form.

\newline

Answer:

Evaluate Definite Integral: Now we evaluate the definite integral from $0$ to $4$ . $\newline$ $\int_{0}^{4}(9e^{0.5x}-2x)dx = [18e^{0.5x} - x^2]_{0}^{4}$ $\newline$ We calculate the value of the antiderivative at the upper limit of integration (x = $4$ ): $\newline$ $18e^{0.5 \cdot 4} - 4^2 = 18e^{2} - 16$
Calculate Upper Limit: Next, we calculate the value of the antiderivative at the lower limit of integration (x = $0$ ): $\newline$ $18e^{0.5 \cdot 0} - 0^2 = 18e^{0} - 0 = 18 \cdot 1 - 0 = 18$
Calculate Lower Limit: We subtract the value of the antiderivative at the lower limit from the value at the upper limit to find the definite integral: $\newline$ $[18e^{2} - 16] - [18]$ $\newline$ $18e^{2} - 16 - 18$ $\newline$ $18e^{2} - 34$