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Greeley [361]
3 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]3 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.

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If the sum of three consecutive numbers is 852, what is the middle one?
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Divide the total by the quantity of numbers:

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Because there are an odd quantity of numbers (3) the answer is the middle number.

The answer is 284

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attashe74 [19]

Answer:

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3 0
3 years ago
Can someone please help me with these?
Vikki [24]

Answer:

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Step-by-step explanation:

One way to find the union of two sets is to list all the elements of both sets in order, then delete any duplicates.

Here, joining the two sets gives ...

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8 0
3 years ago
Solve for x: 150=50e^7x
Mademuasel [1]

Answer:

A

Step-by-step explanation:

150 = 50 {e}^{7x}  \\  50{e}^{7x}  = 150 \\  {e}^{7x}  =  \frac{150}{50}  \\  {e}^{7x}  = 3 \\  ln{e}^{7x}  =  ln(3)  \\ 7x =  ln(3)  \\ x =  \frac{ ln(3) }{7}

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