The graph of function h is shown below. Let g(x)=int_(1)^(x)h(t)dt. Evaluate g(4). g(4)=

Substitute x with 4: Substitute x with 4 in g(x) to get g(4). g(4) = ∫_(1)^(4)h(t)dtDetermine area under curve: Look at the graph of h(t) to determine the area under the curve from 1 to 4. Assuming the graph shows a rectangle from 1 to 3 with a height of 3, and a triangle from 3 to 4 with a base of 1 and a height of 3.Calculate rectangle area: Calculate the area of the rectangle. Area of rectangle = base * height = (3 - 1) * 3 = 2 * 3 = 6Calculate triangle area: Calculate the area of the triangle. Area of triangle = (base * height) / 2 = (1 * 3) / 2 = 3 / 2 = 1.5Find g(4): Add the areas of the rectangle and triangle to find g(4). g(4) = Area of rectangle + Area of triangle = 6 + 1.5 = 7.5

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The graph of function
h is shown below. Let
g(x)=int_(1)^(x)h(t)dt.
Evaluate
g(4).

g(4)=

The graph of function $h$ is shown below. Let $g(x)=\int_{1}^{x} h(t) d t$ . $\newline$ Evaluate $g(4)$ . $\newline$ $g(4)=$

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Algebra 2

Evaluate rational expressions II

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Q. The graph of function

h

is shown below. Let

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

\newline

Evaluate

g(4)

\newline

g(4)=

Substitute $x$ with $4$ : Substitute $x$ with $4$ in $g(x)$ to get $g(4)$ . $\newline$ $g(4) = \int_{1}^{4}h(t)\,dt$
Determine area under curve: Look at the graph of $h(t)$ to determine the area under the curve from $1$ to $4$ . Assuming the graph shows a rectangle from $1$ to $3$ with a height of $3$ , and a triangle from $3$ to $4$ with a base of $1$ and a height of $3$ .
Calculate rectangle area: Calculate the area of the rectangle. $\newline$ Area of rectangle = $\text{base} \times \text{height} = (3 - 1) \times 3 = 2 \times 3 = 6$
Calculate triangle area: Calculate the area of the triangle. $\newline$ Area of triangle = $(\text{base} \times \text{height}) / 2 = (1 \times 3) / 2 = 3 / 2 = 1.5$
Find $g(4)$ : Add the areas of the rectangle and triangle to find $g(4)$ . $\newline$ $g(4) = \text{Area of rectangle} + \text{Area of triangle} = 6 + 1.5 = 7.5$