Please help with the questions on definite integrals.

Haru

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Joined
Dec 25, 2019
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6
Hello, I am Haru and I have difficulties to solve the following problems. It would be much appreciated if someone can help me. Sorry for asking so many questions. And wish you Merry Christmas.

Let
condition 1:

f(x) = 0 ..................................if x is smaller than -3;

f(x) = 3 .................................if x larger or equal to -3 but smaller than 1;

f(x) = -4 ................................if x is larger than or equal to 1 but smaller than 5;

f(x) = 0 ................................ if x is larger or equal to 5
and
condition 2:

g(x)= ∫ f(t)dt (which the lower bound (from): -3 and the upper bound (to): x)

~ For this question, I am not able to find the value of g(2), g(6) and I do not know how to plot a graph of g(x). As a result, I am not able to find the absolute maximum of g(x).
 
Hello, I am Haru and I have difficulties to solve the following problems. It would be much appreciated if someone can help me. Sorry for asking so many questions. And wish you Merry Christmas.

Let
condition 1:

f(x) = 0 ..................................if x is smaller than -3;

f(x) = 3 .................................if x larger or equal to -3 but smaller than 1;

f(x) = -4 ................................if x is larger than or equal to 1 but smaller than 5;

f(x) = 0 ................................ if x is larger or equal to 5
and
condition 2:

g(x)= ∫ f(t)dt (which the lower bound (from): -3 and the upper bound (to): x)

~ For this question, I am not able to find the value of g(2), g(6) and I do not know how to plot a graph of g(x). As a result, I am not able to find the absolute maximum of g(x).
Plot f(x) first. You are given f(x) = constant for several discrete domains. What does the plot of f(x) look like?
 
The areas are just rectangles. Did you plot the graph? Do you know what an integral means? Do you know how to find the area of a rectangle? Might this course be a bit too advanced for you?
 
See if you can work out values of g(4), g(-2), g(0), g(1), g(-1) and g(5) and plot the graph of g(x).
 
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