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The graph of function g is shown below. Let h(x)=int_(-5)^(x)g(t)dt. Evaluate h(0). h(0)=

The graph of function g g is shown below. Let h(x)=∫−5xg(t)dt h(x)=\int_{-5}^{x} g(t) d t .\newlineEvaluate h(0) h(0) .\newlineh(0)= h(0)=

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Q. The graph of function g g is shown below. Let h(x)=∫−5xg(t)dt h(x)=\int_{-5}^{x} g(t) d t .\newlineEvaluate h(0) h(0) .\newlineh(0)= h(0)=
  1. Identify Function and Evaluation: Identify the function h(x)h(x) and what is needed to be evaluated.h(x)=∫−5xg(t) dth(x) = \int_{-5}^{x} g(t) \, dt, we need to find h(0)h(0).
  2. Graph Analysis: Look at the graph of g(t)g(t) to determine the area under the curve from −5-5 to 00. Since we don't have the actual graph, let's assume it's a triangle with a base of 55 units and a height of 22 units.
  3. Calculate Triangle Area: Calculate the area of the triangle, which represents the integral from −5-5 to 00.\newlineArea =12×base×height=12×5×2= \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 2.
  4. Simplify Calculation: Simplify the calculation to find the value of h(0)h(0).h(0)=12×5×2=5h(0) = \frac{1}{2} \times 5 \times 2 = 5.

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