Question

Determine l=
∫2exdx
,given that l=50.2 when x =3

Answer 1

Answer on Question #45745 – Math – Integral Calculus

Determine $I = \int 2e^{x}dx$, given that $I = 50.2$, when $x = 3$.

Solution.

First of all we will find the indefinite integral:

$$I = \int 2e^{x}dx = 2\int e^{x}dx = 2e^{x} + C.$$

We know, that $I = 50.2$, when $x = 3$. Hence, we can use this condition to calculate the constant $C$:

$$50.2 = 2e^{3} + C,$$ $$C = 50.2 - 2e^{3}.$$

$e \approx 2.7183$, then $e^{3} \approx 20.1$. It we can find with help of calculator.

Now we can evaluate $C$:

$$C = 50.2 - 2 \cdot 20.1 = 50.2 - 40.2 = 10.$$

Answer:

hence, our indefinite integral $I = 2e^{x} + 50.2 - 2e^{3}$ (approximately $I = 2e^{x} + 10$).

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