Question

1. Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. Between y = x^3 and y = −1 for x in [−1, 1]. (THE ANSWER IS 2 BUT I DONT UNDERSTAND WHY)

2. Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer.

Between y = x and y = x² for x in [−2, 1]

3. Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. (I KEEP GETTING -3/10, BUT THE ANSWER IS 3/10. I KEEP GETTING NEGATIVE AND I DONT KNOW WHY)

Enclosed by y = −x and y = x⁴   

4. Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. (THE ANSWER IS 8/15, BUT I KEEP GETTING NEGATIVE -8/15, PLEASE HELP!)

Enclosed by y = −x⁴ + x² and y = −x² + x⁴   

Answer 1

1)   So the graph of y=-1 and y=x^3 is as

As we see the intersection point is (1,1)

And we need to find area between x=-1 and 1

Hence area is

Where f(x)=y=x^3 as this is above the other curve

g(x)=y=-1