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The graph of function
g is shown below. Let
h(x)=int_(-1)^(x)g(t)dt.
Evaluate
h(3).

h(3)=

The graph of function $g$ is shown below. Let $h(x)=\int_{-1}^{x} g(t) d t$ . $\newline$ Evaluate $h(3)$ . $\newline$ $h(3)=$

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Evaluate exponential functions

Full solution

Q. The graph of function

g

is shown below. Let

h(x)=\int_{-1}^{x} g(t) d t

.

\newline

Evaluate

h(3)

.

\newline

h(3)=

Assumption of Provided Graph: Since we don't have the actual graph of $g(t)$ , we'll assume it's been provided and that we can determine the area under the curve from $-1$ to $3$ . Let's say the area from $-1$ to $3$ is $A$ . So, $h(3)$ will be equal to $A$ .
Calculation of Area: Now, we calculate the area $A$ . If the graph is made up of simple geometric shapes, we can calculate the area of each shape and sum them up. Let's say the total area we found is $15$ square units.
Calculation of $h(3)$ : So, $h(3)$ is equal to the total area under the graph of $g(t)$ from $-1$ to $3$ , which we've calculated as $15$ .

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