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

The graph of function g g is shown below. Let f(x)=∫−3xg(t)dt f(x)=\int_{-3}^{x} g(t) d t .\newlineEvaluate f(1) f(1) .\newlinef(1)= f(1)=

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Full solution

Q. The graph of function g g is shown below. Let f(x)=∫−3xg(t)dt f(x)=\int_{-3}^{x} g(t) d t .\newlineEvaluate f(1) f(1) .\newlinef(1)= f(1)=
  1. Define f(x)f(x): Understand the definition of f(x)f(x).f(x)f(x) is the definite integral of g(t)g(t) from −3-3 to xx.
  2. Evaluate f(1)f(1): Evaluate f(1)f(1).\newlineTo find f(1)f(1), we need to calculate the definite integral of g(t)g(t) from −3-3 to 11.
  3. Determine area under curve: Look at the graph of g(t)g(t) to determine the area under the curve from −3-3 to 11. Since we don't have the graph, we'll assume it's been provided and we can find the area directly from it.
  4. Calculate area AA: Calculate the area under g(t)g(t) from −3-3 to 11. Let's say the area under g(t)g(t) from −3-3 to 11 is AA.
  5. Find f(1)f(1): The area AA represents the value of the integral, which is f(1)f(1).\newlineSo, f(1)=Af(1) = A.

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