Mathematics, 14.01.2020 21:31 ggujjnh

Exercise is mixed —some require integration by parts, while others can be integrated by using techniques discussed in the chapter on integration.
∫x^3ex^4 dx.

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Answer from: freeman36

$\displaystyle \int {x^3e^{x^4}} \, dx = \frac{e^{x^4}}{4} + C$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

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

$\displaystyle \int {x^3e^{x^4}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u: $\displaystyle u = x^4$ [u] Basic Power Rule: $\displaystyle du = 4x^3 \ dx$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int {x^3e^{x^4}} \, dx = \frac{1}{4} \int {4x^3e^{x^4}} \, dx$ [Integral] U-Substitution: $\displaystyle \int {x^3e^{x^4}} \, dx = \frac{1}{4} \int {e^{u}} \, dx$ [Integral] Exponential Integration: $\displaystyle \int {x^3e^{x^4}} \, dx = \frac{e^{u}}{4} + C$ [u] Back-Substitute: $\displaystyle \int {x^3e^{x^4}} \, dx = \frac{e^{x^4}}{4} + C$

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

Unit: Integration

Answer from: Quest

4 packs of water and 7 packs of candy bars

step-by-step explanation:

35x4=140

140/20=7

Answer from: Quest

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2 is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes. our only condition is that it passes through the point (-2,5)

A. write an equation of a line that passes through (-2, 5). b. how many different equations could y

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