|(-2x) - edx, but substi-Explain why you can use the substitution method to evaluatetution cannot be used to evaluatedx.In fact, there is no specific antiderivative for e-! That doesn't seem normal, does it?

We have to discuss the integrals: ∫-2x. e-x2dx We can use substitution method because derivatives of…

Explain why you can use the substitution method to evaluate |(-2x) · e- dx, but substi- tution cannot be used to evaluate dr. In fact, there is no specific antiderivative for e-! That doesn't seem normal, does it?

Explain why you can use the substitution method to evaluate |(-2x) · e- dx, but substi- tution cannot be used to evaluate dr. In fact, there is no specific antiderivative for e-! That doesn't seem normal, does it?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter0: A Review Of Basic Algebra

Section0.4: Polynomials

Problem 129E

See similar textbooks

Related questions

Q: log 3= x loghs y log1s j tye. Show in x ad ニ

A: Given, log9=x and log4=y

Q: Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and val...

A: Given data: The rate of oil at t=0 is r1(t)=8.7 L/h. The rate of oil at t=2 is r2(t)=7.9 L/h. Th...

Q: Can someone help me to simplify this derivative? H and D are constants, and I have done the first st...

A: To Determine: we have a function then find the derivative Given: we have a function Z(x)=Hxx-D2+x2 E...

Q: This exercise uses the population growth model. A certain culture of the bacterium Rhodobacter sphae...

A: Definition used - Exponential growth model - A=A0ekt ...

Q: Find the radius of convergence for 2 ·4 ·6 · ... · (2n) x". (2n)! n=1 Preview

A: The power series is given as, S=∑n=1∞2·4·6·…………2n2n!xn Rearrange the terms, S=∑n=1∞2n1·2·3·…………n2n!x...

Q: Suppose you deposit $6,000 at 5% interest compounded continuously. Find the average value of your ac...

Q: Evaluate / zev dr.

A: Given: ∫xexdx

Q: If f(x) = ∫0 x (1 - t^2)e^t^2 dt , on what interval is f increasing?

A: To determine the interval on which f is increasing. f(x)=∫0x(1-t2)et2dt

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving...

A: Given: y= 36-x2 To find: Volume of solid formed by revolving the region about the y - axis.

Q: Find a model for simple harmonic motion satisfying the specified conditions. Displacement, d (t = 0)...

A: Given, At t= 0, displacement =7 inches Amplitude, a = 7 inches. Per...

Q: Find the area between the curves y = 3 x and y = x2 9: Exact value, show all work for full credit.

A: Given curves are, y=3x and y=9x2.

Q: I am stuck

A: Given time = 16 years rate =6% compounded monthly

Q: Find the radius of convergence of the power series. (If you need to use co or -oo, enter INFINITY or...

A: Given ∑n=0∞-1nxn8n

Q: The vectors F and G represent two forces acting on an object, as indicated in the following figure. ...

Q: Solve the differential equation and initial condition and verify that your answer satisfies both the...

Q: 6. by competitors, Pizza Hut is losing customers and consequently the number of stores remaining ope...

A: Given in the year 2015, the no. of pizza hut stores was 2178 and it is decreasing by 11% each year.

Q: Determine whether the geometric series is convergent or divergent. 10 2 + 0.4 0.08 + -. O convergent...

A: Given geometric series is : 10 -2 +.4 -0.08 +.... Common ratio, r = -0.2

Q: Evaluate the limit of f(x) numerically or state that the limit does not exist. tan-'(5x) cos-'(x) S(...

A: Given that ; The function is f (x) = tan -1 ( 5x)cos -1 (x) . As we know exponent rule1ba=b-a As we ...

Q: F(x)=7x-8 and g(x)= 3-x^2 what is f(g(0)) and g(f(0))

Q: sec 10.1

A: It is given that in△BCA; ∠A=25°, ∠C=90° from given diagram and AC=190cmWe have t...

Q: x+ kx - 24 x2-x-12 Consider the function G(x): to answer the following. A. Determine for which value...

A: Note: There are many subparts in the given question. So I will answer the first three of them and th...

Q: Solve the triangle with sides a = 6 and b 4 and included angle C = 76°. %3D

Q: Find the equations of (1) tangent plane and (2) the normal line to the given surface at the specifie...

A: Equation of tangent plane at x0, y0, z0 is, z-z0=∂z∂xx-x0+∂z∂yy-y0 Equation of a line with normal ve...

Q: Find the equation of the line in standard form (i.e., y = mx + b) that conatins the point (-3,5) and...

A: We have to find the equation of line in standard form if it is passing through the point -3, 5 and i...

Q: The equation cos x = x has exactly one solution. (a) Use a graph to show that the equation cos x = 0...

A: (a) The graph of fx=cosx and gx=sinx is shown below, From the above graph it is clear that the two ...

Q: Q1.Find the solution of the recurrence relationan 5ал-1 — 6ал-2whereao 3D 4anda, = 1. %D %3D

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new quest...

Q: Find the intervals of concavity and determine if there are any inflection points. If not, explain. f...

A: we have to find the intervals of concavity and also we have to determine the inflection point of a ...

Q: Use chain rule

Q: Solve for the following differential equations

A: The differential equation is y'-1x2y=x3y2. It is in the form of a Bernoulli ordinary differential eq...

Q: If sinx = siny = a and cosx = cosy = b,then cos(x-y) is

Q: Procedure please

A: Consider the given function as ddx∫2x2+3cos2xdx

Q: A gardener is designing a rectangular planter for a rose garden in front of the administration build...

A: Concept: The calculus helps in understanding the changes between values that are related by a functi...

Q: Using the right endpoints, find an expression for the area under the graph of f as a limit. Do not e...

A: here the given function is f(x)= sinx, 0≤x≤π lower limit a=0 upper limit b=π let there are 4 re...

Q: 3. The population of wolves on an island can be modeled by the equation P(t) = 120e6 where t is the ...

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C f...

Question

|(-2x) - e
dx, but substi-
Explain why you can use the substitution method to evaluate
tution cannot be used to evaluate
dx.
In fact, there is no specific antiderivative for e-! That doesn't seem normal, does it?

Expert Solution

Step 1

We have to discuss the integrals:

$\int (- 2 x) . e^{- x^{2}} d x$

We can use substitution method because derivatives of $- x^{2}$ is present in the integral as $- 2 x$

Therefore,

let $t = - x^{2}$

differentiating both sides with respect to $' x'$ , we get

$\begin{array}{rcl} \frac{d t}{d x} & = & \frac{d (- x^{2})}{d x} \\ \frac{d t}{d x} & = & - 2 x \\ d t & = & - 2 x d x \end{array}$

Step by step

Solved in 2 steps

Knowledge Booster

$Indefinite Integral$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.