1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dmitrij [34]
3 years ago
11

Which of the following integrals cannot be evaluated using a simple substitution?

Mathematics
2 answers:
vitfil [10]3 years ago
7 0
The third one, not sure about any other ones.
Burka [1]3 years ago
5 0

The integral \boxed{\int {{x^2}{e^{{x^2}}}dx} } cannot be evaluated by using a simple substitution.Option (c) is correct.

Further explanation:

Given:

The integrals are as follows,

(a). \int {x{e^{{x^2}}}dx}

(b). \int {{e^{\left( {2x + 3} \right)}}dx}

(c). \int {{x^2}{e^{{x^2}}}dx}

(d). None of these.

Explanation:

Option (a)

The integral is I = \int {x{e^{{x^2}}}dx}.

Substitute t for {x^2} in integral I = \int {x{e^{{x^2}}}dx}.

\begin{aligned}{x^2} &= t\\2xdx &= dt\\\end{aligned}

The integral can be obtained as follows,

\begin{aligned}I&= \int {{e^t}dt}\\&= {e^t} + C\\&= {e^{{x^2}}} + C\\\end{aligned}

Option (a) can be evaluated by simple substitution.

Option (b)

The integral is \int {{e^{\left( {2x + 3} \right)}}dx}

The integral can be obtained as follows,

\begin{aligned}I&= \int {{e^{\left( {2x + 3} \right)}}dx}\\&= \frac{1}{2} \times {e^{\left( {2x + 3} \right)}} + C\\\end{aligned}

Option (b) can be evaluated by simple substitution.

Option (c)

The integral is I = \int {{x^2}{e^{{x^2}}}dx}.

Substitute t for {x^2} in integral I = \int {{x^2}{e^{{x^2}}}dx}.

\begin{aligned}{x^2}&= t \\2xdx &= dt\\\end{aligned}

The integral can be obtained as follows,

I = \int {\sqrtt  \times {e^t}dt}

Option (c) cannot be evaluated by simple substitution as we have to use integration by parts.

The integral \boxed{\int {{x^2}{e^{{x^2}}}dx} } cannot be evaluated by using a simple substitution.Option (c) is correct.

Learn more:

  1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
  2. Learn more about equation of circle brainly.com/question/1506955.
  3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: integral, evaluated, simple substitution, integration, differentiation, exponential.

You might be interested in
The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of x if the shortest side, y, meas
kicyunya [14]
An isosceles triangle has 2 sides of the same length and one side that's not the same length.

So it says the shortest side, y, is 2.1m, so that means it's the side that is not the same length as the other two sides.

But the other two sides will be the same length. Let's make those 2 sides x.

The equation would be
x + x + 2.1 = 7.5

And with that you can find x.
3 0
3 years ago
Read 2 more answers
Please Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Oduvanchick [21]

Answer:

26:26

Step-by-step explanation:

I hope I've helped :)

4 0
3 years ago
Find the complement and the supplement of the given angle.<br> 23°
e-lub [12.9K]

Answer:

Complement: 67°

Supplement: 157°

Step-by-step explanation:

Complementary angles = 90°

90-23=67°

Supplementary angles = 180°

180-23=157°

7 0
3 years ago
Maria makes $16 per hour. She gets a 18% raise. What is her new hourly<br> rate?
Mariana [72]

Answer:

$18.88 per hour.

Step-by-step explanation:

We first need to find 18% of $16.

16 * 0.18 = 2.88

The pay rate increases by $2.88.

$16 + $2.88 = $18.88

Hope this helps.

8 0
2 years ago
Find the product ( 1 1+1 ) ( 2 2+1 ) ( 3 3+1 )….. ( +1 ) for k=6
Sedaia [141]
34=97+29=195 and this is your answer
6 0
3 years ago
Other questions:
  • Do 0.3 and 3.0 have the same value. Explain.<br><br> Explain=10 points
    8·1 answer
  • Which function represents exponential growth?
    11·1 answer
  • Which expression is equivalent to b^m x b^n? A. b^m+n B. b^m-n C. b^mx n D. b^m/n
    12·2 answers
  • Create an equivalent ratio to 35:40 by dividing both sides by 5. What is the equivalent ratio?
    11·2 answers
  • 4/f + 11 =29 what does f =
    10·2 answers
  • Which statement is true regarding DC current?
    14·2 answers
  • Help me do this question ​
    7·1 answer
  • The perimeter of the rectangle below is 42 inches. Find the value of x.
    6·1 answer
  • Question 9
    15·1 answer
  • How do I solve this?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!