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3 years ago

Evalute this integral

Mathematics

1 answer:

enot [183]3 years ago

4 0

Answer:

(1/2)sin(2x) + C

Step-by-step explanation:

$y=2x\\\frac{dy}{dx} =2\\\ dx=\frac{dy}{2} \\\int\limits {cos 2x} \, dx \\\int\limits {cos(y) } \, \frac{dy}{2} =\frac{1}{2} \\\int\limits {cos(y) } \, dy=\frac{1}{2}sin(y) \\ substitute / y=2x\\\int\limits {cos 2x} \, dx = \frac{1}{2}sin(2x) +C$

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monitta

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3 years ago

Integrate x+1/sqrt(x). I know that the answer is 2/3 • sqrt(x) • (x+3) + C, but I don't know how it is simplified from 2/3 • x^3

Andreas93 [3]

$\displaystyle\int\frac{x+1}{\sqrt x}\,\mathrm dx=\int\frac x{x^{1/2}}+\frac1{x^{1/2}}\,\mathrm dx$

$=\displaystyle\int x^{1/2}+x^{-1/2}\,\mathrm dx$

By the power rule,

$=\dfrac{x^{3/2}}{\frac32}+\dfrac{x^{1/2}}{\frac12}+C$

(this seems to be the step you're not getting?)

$=\dfrac23x^{3/2}+2x^{1/2}+C$

The next step is to pull out a common factor of $x^{1/2}$ from the antiderivative:

$x^{3/2}=x^{1/2+1}=x^{1/2}\cdot x^1$

so that the final result is

$\dfrac23x^{3/2}+2x^{1/2}+C=\dfrac23x^{1/2}(x+3)+C$

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3 years ago

A ball is shot straight up into the air from the ground with initial velocity of 45ft/sec. Assuming that the air resistance can

Nesterboy [21]

V2^2 = V1^2 - 2gh

<span>=> 0 = 44^2 - 2 (32.2) h </span>

<span>=> h = 44^2 / 64.4 = 30.062 ft</span>

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3 years ago

.54545454 as a fraction

defon

The answer as a fraction is 6/11

4 0

3 years ago

Does anyone mind helping?

lorasvet [3.4K]

Answer:

x^2 y^12

Step-by-step explanation:

( x ^ 1/2 * y ^3 ) ^ 4

A power raised to a power has the exponents multiplied

a^b^c = a^ (b*c)

x^ 1/2 ^ 4 * y^3^4

x^(1/2*4) * y^(3*4)

x^2 y^12

6 0

3 years ago

Read 2 more answers