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tatuchka [14]
3 years ago
12

the area of the region bounded by the curve y=e^2x the x axis the y axis and the line x=2 is equal toA) e^4/2 -e B) e^4/2 - 1 C)

e^4/2 - 1/2 D) 2e^4 -e E) 2e^4 -2

Mathematics
1 answer:
klemol [59]3 years ago
5 0

Answer:b

Step-by-step explanation:

Given

y=e^{2x}

Area bounded by y=e^{2x}, y=0,\ x=0\ and\ x=2 is shown by shaded area in the diagram

Area=A=\int_{0}^{2}ydx

A=\int_{0}^{2}e^{2x}dx

A=\left [ \frac{e^{2x}}{2}\right ]^{2}_{0}

A=\frac{1}{2}\left [ e^4-e^0\right ]

A=\frac{e^4}{2}-1

thus option b is correct

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Can you be certain? Only by mathematically proving that the shape has the identifying properties of a parallelogram can you be sure. You can prove this with either a two-column proof or a paragraph proof.

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Prove that opposite sides are congruent

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We can use one of these ways in a two-column proof. Bear in mind that, to challenge you, most problems involving parallelograms and proofs will not give you all the information about the presented shape. Here, for example, you are given a quadrilateral and told that its opposite sides are congruent.

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Paragraph Proof

You can also use the paragraph proof form for any of the six ways. Paragraph proofs are harder to write because you may skip a step or leave out an explanation for one of your statements. You may wish to work very slowly to avoid problems.

Always start by making a drawing so you know exactly what you are saying about the quadrilateral as you prove it is a parallelogram.

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