(a) The integral is equal to the area of the triangle; it has height 20 and base 10, so the area is 20*10/2 = 100.
(b) The integral is equal to the area of the semicircle with radius 10. It's also under the horizontal axis, so the area is negative. The semicircle has area 
, so the integral is -50π.
(c) First compute
which is the area of the triangle on the right. It has height and base 5, so its area is 25/2.
Then split up the desired integral as
and plug in the integral values you know:
Answer:
This is equation of ellipse
Step-by-step explanation:
we are given
We can see that right side is 36
so, we can make right side as 1 by dividing both sides by 36
we can simplify it
we can rewrite it as
now, we can compare it with standard equation of ellipse
we can see that both equations are similar
so, this is equation of ellipse
For this case we have that by definition:
So:
We apply distributive property that states that:
In addition, we take into account that:
Answer:
Option B
Answer:
54 units squared
Step-by-step explanation:
You have to divide the shape into simpler shapes such as rectangles and triangles that you can easily find the area of. Then, add those areas together. I divided it into one rectangle and three triangles.
Rectangle 1: length=7 width=6 6(7)=42
Triangle 1: base=6 height=2 1/2(6)2=6
Triangle 2: base=3 height=2 1/2(3)2=3
Triangle 3: base=6 height=1 1/2(6)1=3
Area= R1+T1+T2+T3= 42+6+3+3= 54 units squared
