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
Greeley [361]
2 years ago
14

Use the graph of f to calculate

ormula1" title="\int\limits^4_0 {f(t)} \, dt" alt="\int\limits^4_0 {f(t)} \, dt" align="absmiddle" class="latex-formula">. PLEASE HELP!

Mathematics
1 answer:
frozen [14]2 years ago
3 0

You should already be aware that the definite integral of f(t) is equivalent to the signed area under the curve of

\displaystyle\int_0^1f(t)\,\mathrm dt

corresponds the area of the triangle on the left, and

\displaystyle\int_1^4f(t)\,\mathrm dt

is the area of the trapezoid in the middle. You should know how to compute the area of these shapes.

We end up with

\displaystyle\int_0^4f(t)\,\mathrm dt=-\frac{1\times2}2+\frac{(1+3)\times2}2=3

since the triangle has height 2 and base 1, and the trapezoid has height 2 with two base lengths 1 and 3.

Edit: The area under the curve is highlighted red in the attachment below. It's the area between the curve and the horizontal axis, but it's also signed, meaning the area <em>below</em> the axis is negative, and the area <em>above</em> the axis is positive.

You might be interested in
What does y = 2.5x - 10 equal?
mariarad [96]

Answer:

Step-by-step explanation:

x= y+10

-----------------

    2.5

3 0
2 years ago
X^2+15x=-45 solve by factoring
Julli [10]

1 Move all terms to one side.

{x}^{2}+15x+45=0

x

2

+15x+45=0

2 Use the Quadratic Formula.

x=\frac{-15+3\sqrt{5}}{2},\frac{-15-3\sqrt{5}}{2}

x=

2

−15+3

5

,

2

−15−3

5

3 Simplify solutions.

x=-\frac{3(5-\sqrt{5})}{2},-\frac{3(5+\sqrt{5})}{2}

x=−

2

3(5−

5

)

,−

2

3(5+

5

)

6 0
3 years ago
Read 2 more answers
For a test of upper h 0h0​: pequals=​0.50, the sample proportion is 0.470.47 based on a sample size of 100. use this information
otez555 [7]
The parts (a) to (c) can be completed using the equtaion y ⇔ Δ ∈ ∞, ㏒Δ ∀ x∈√a, a∈R.
8 0
3 years ago
A circle with radius of 6 cm sits inside a circle with radius of 9 cm. What is
laiz [17]

Answer:

area of Circle = (pi)r^2

3.14×4

12.56

7 0
3 years ago
Which is the better deal?
aliina [53]

Answer:

36 oz

Step-by-step explanation:

Get the other options down to 12oz units for their price and then you can compare which one is the cheapest for 12oz.

12oz = $1.99

36oz/3 = 12oz   so $2.59/3   = $ .86

48oz/4= 12oz   so $3.99/4  = $1.00

60oz/5= 12oz   so $4.59/5 = $ .92

So looking at the breakdown, the 36oz one is the cheapest because for that price for a third of it comes out to .86 cents.

3 0
3 years ago
Other questions:
  • The surface area of rectangular prism is 48 ft.². The area of its front is 4 ft.², and the area of one side is 10 ft.². What is
    8·1 answer
  • How much interest would be earned on $3,700 in one year if it is invested at 4%?
    8·1 answer
  • Pls help me with this answer choice question! brainliest, rattings, thanks etc.
    7·1 answer
  • Jeans ($48) Sweater ($42) Tennis Shoes ($69) T-Shirt ($21) Blouse ($52) Heather is shopping for back-to-school clothes. The item
    10·2 answers
  • Apply the distributive property<br><br> 1/4(16a+8b+c)
    11·1 answer
  • How do you write mixed numbers or fractions as decimals?
    14·1 answer
  • The beginning checkbook balance of Gregory Co. was $3,045.58. Their bank statement indicated a balance of $4,262.92. The bookkee
    10·1 answer
  • What is the value of x?
    13·1 answer
  • How do you find the surface area of a cube
    5·1 answer
  • A circle with circumference 130 has an arc with a 72°<br> angle. What is the length of the arc?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!