Mathematics, 03.08.2019 23:30, blxxmgrxcie

30pts! brainliest! calculus 2! definite integral of (e^(1/x))/(4x^2) * dx show clear work and steps for award! you so much!

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answered: browndariel

$\displaystyle \int {\frac{e^\big{\frac{1}{x}}}{4x^2}} \, dx = \frac{-e^\big{\frac{1}{x}}}{4} + C$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]: $\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Integration

Integrals[Indefinite Integrals] Integration Constant C

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int {\frac{e^\big{\frac{1}{x}}}{4x^2}} \, dx$

Step 2: Integrate Pt. 1

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int {\frac{e^\big{\frac{1}{x}}}{4x^2}} \, dx = \frac{1}{4}\int {\frac{e^\big{\frac{1}{x}}}{x^2}} \, dx$

Step 3: Integrate Pt. 2

Identify variables for u-substitution.

Set u: $\displaystyle u = \frac{1}{x}$ [u] Differentiate [Derivative Rules, Basic Power Rule]: $\displaystyle du = \frac{-1}{x^2} \ dx$

Step 4: Integrate Pt. 3

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int {\frac{e^\big{\frac{1}{x}}}{4x^2}} \, dx = \frac{-1}{4}\int {\frac{-e^\big{\frac{1}{x}}}{x^2}} \, dx$ [Integral] U-Substitution: $\displaystyle \int {\frac{e^\big{\frac{1}{x}}}{4x^2}} \, dx = \frac{-1}{4}\int {e^\big{u}} \, du$ [Integral] Exponential Integration: $\displaystyle \int {\frac{e^\big{\frac{1}{x}}}{4x^2}} \, dx = \frac{-1}{4}e^\big{u} + C$ Simplify: $\displaystyle \int {\frac{e^\big{\frac{1}{x}}}{4x^2}} \, dx = \frac{-e^\big{u}}{4} + C$ Back-Substitute: $\displaystyle \int {\frac{e^\big{\frac{1}{x}}}{4x^2}} \, dx = \frac{-e^\big{\frac{1}{x}}}{4} + C$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

answered: Guest

step-by-step explanation:

dong do iy iys a scram

answered: Guest

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

Me? ! with this question which relationship is a function?

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30pts! brainliest! calculus 2! definite integral of (e^(1/x))/(4x^2) * dx show clear work and st...