Question

Calculus II question. Just need help with set up (problem in picture).

Answer 1

I know how to graph it. How do I set up to solve the part in yellow?

Answer 2

i dont know it i wish i could help

Answer 3

You didn't have to take the time to tell me you didn't know it.

Answer 4

Over the interval \([-3,0]\), you have the equation of a quarter circle (the third quadrant of a circle centered at the origin with radius 3, to be specific). Since this area lies below the x-axis, you'll have a "negative area."

The other interval, \([0,5]\), is a set of triangles. If you know the formulas for both shape type areas, you can find the value of the definite integral without antidifferentiating.

Answer 5

Would that be the only way?

Answer 6

Hmm, maybe approximating the area using a Riemann sum. That wouldn't use the antiderivative, but it's certainly not the most efficient way. I think the geometric interpretation is your best bet here, especially considering it's just a matter of adding/subtracting areas of basic shapes.