How do you sketch the region whose signed area is represented by the definite integral, and evaluate the integral using an appropriate formula from geometry, where needed.

integral 0, 3 x dx
integral -2,-1 x dx
integral -1,4 x dx
integral -5,5 x dx

I don't really understand the question.

Question

How do you sketch the region whose signed area is represented by the definite integral, and evaluate the integral using an appropriate formula from geometry, where needed.

integral 0, 3 x dx
integral -2,-1 x dx
integral -1,4 x dx
integral -5,5 x dx

I don't really understand the question.

wesdg1978 · Answer

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anonymous · Answer

Draw the graph and shade the region under the graph and above the x-axis between $x=0$ and $x=3$

anonymous · Answer

the definite integral corresponds to the area of that region

wesdg1978 · Answer

What graph? Do you mean y=x or something else?

anonymous · Answer

that is the function being integrated in each example so yes...

wesdg1978 · Answer

So then what does it mean to evaluate the integral using an appropriate formula from geometry?