1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
IgorLugansk [536]
3 years ago
13

Evaluating integral by net area

Mathematics
1 answer:
N76 [4]3 years ago
8 0

The graph of f(x)=2 is a horizontal line. So the area under f(x) on [0, 8] is equal to the area of a rectangle with length 8 and height 2, or 16.

The graph of g(x)=\sqrt{64-x^2} is the upper half of a circle with radius \sqrt{64}=8. It's symmetric about x=0, so on the interval [0, 8], we're considering a quarter of the circle. The area of such a sector is \frac{\pi 8^2}4=16\pi.

Then use the fact that the definite integral is distributive over sums, meaning

\displaystyle\int_0^8f(x)+g(x)\,\mathrm dx=\int_0^8f(x)\,\mathrm dx+\int_0^8g(x)\,\mathrm dx=16+16\pi

You might be interested in
Bill must take an 8-question true/false quiz and has to guess on each problem. How many
MrMuchimi

Answer:40320

Step-by-step explanation:

8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320 and there are 8 questions total

6 0
3 years ago
<img src="https://tex.z-dn.net/?f=6%5Csqrt%7B3%7D%2B2%281-%5Csqrt%7B27%7D%29%3D2" id="TexFormula1" title="6\sqrt{3}+2(1-\sqrt{27
skelet666 [1.2K]

Answer:

This is true.

Step-by-step explanation:

Step 1: see that √27 is the same as √3*3*3 and thus 3√3

Step 2: remove parenthesis so that 2(1-3√3) becomes 2 - 6√3

Step 3: observe that the equation now becomes 6√3 + 2 - 6√3 = 2

if you simplify any further, you are left with 0=0, which is true.

Comment if there is any step that requires more details...

3 0
3 years ago
Read 2 more answers
Is √55.5(-0.45.6)-78% an irrational number
Lynna [10]

Answer:

no

Step-by-step explanation:

7 0
3 years ago
You are given an n×n board, where n is an even integer and 2≤n≤30. For how many such boards is it possible to cover the board wi
faltersainse [42]

Answer:

  7

Step-by-step explanation:

The number of cells in a tile is 4. If colored alternately, there are 3 of one color and 1 of the alternate color. To balance the coloring, an even number of tiles is needed. Hence the board dimensions must be multiples of 4.

In the given range, there are 7 such boards:

  4×4, 8×8, 12×12, 16×16, 20×20, 24×24, and 28×28

3 0
3 years ago
THIS QUESTION IS WORTH 33 POINTS!! PLEASE PLEASE HELP ME
3241004551 [841]
It's less than a whole number like 2/1 times 1/2 is 2/2 or 1
6 0
3 years ago
Read 2 more answers
Other questions:
  • Again we have two methods, A and B, available for teaching a certain industrial skill. There is an 80% chance of successfully le
    7·1 answer
  • How do you evaluate the following equation by distributing the negative sign?
    13·1 answer
  • 100/h , for h = -25 i need in a sentence
    5·1 answer
  • 87 is 15% of what number​
    7·2 answers
  • You have 50 blueberry scones and 75 cranberry scones. You want to make as many identical bags as possible. Each bag should have
    12·2 answers
  • Solve each please and tell me which have an equivalent expression
    12·1 answer
  • Help please!!!! I’m confused
    15·1 answer
  • If 35% of a number is 140 what is that number
    13·1 answer
  • PLEASE CAN SOMEONE HELP I HAVE 5 mins
    11·1 answer
  • What are the solutions to the quadratic equation 2x2 + 10x - 48 = 0?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!