Mathematics : asked on lasardia
 09.04.2023

The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent. 6x^5(x^6-2)dx

. 0

Step-by-step answer

24.06.2023, solved by verified expert
Unlock the full answer

The indefinite integral can be found in more, №17886891, 09.04.2023 20:39 = The indefinite integral can be found in more, №17886891, 09.04.2023 20:39

Step-by-step explanation:

To find:

The indefinite integral can be found in more, №17886891, 09.04.2023 20:39

Solution:

Method of substitution:

Let The indefinite integral can be found in more, №17886891, 09.04.2023 20:39

Differentiate both sides with respect to The indefinite integral can be found in more, №17886891, 09.04.2023 20:39

The indefinite integral can be found in more, №17886891, 09.04.2023 20:39

[use The indefinite integral can be found in more, №17886891, 09.04.2023 20:39]

So,

The indefinite integral can be found in more, №17886891, 09.04.2023 20:39 = ∫ The indefinite integral can be found in more, №17886891, 09.04.2023 20:39 = The indefinite integral can be found in more, №17886891, 09.04.2023 20:39 where The indefinite integral can be found in more, №17886891, 09.04.2023 20:39 is a variable.

(Use ∫The indefinite integral can be found in more, №17886891, 09.04.2023 20:39 )

Put The indefinite integral can be found in more, №17886891, 09.04.2023 20:39

The indefinite integral can be found in more, №17886891, 09.04.2023 20:39 = The indefinite integral can be found in more, №17886891, 09.04.2023 20:39

Use The indefinite integral can be found in more, №17886891, 09.04.2023 20:39

So,

The indefinite integral can be found in more, №17886891, 09.04.2023 20:39 = The indefinite integral can be found in more, №17886891, 09.04.2023 20:39

where The indefinite integral can be found in more, №17886891, 09.04.2023 20:39

Without using substitution:

The indefinite integral can be found in more, №17886891, 09.04.2023 20:39 = ∫The indefinite integral can be found in more, №17886891, 09.04.2023 20:39 = The indefinite integral can be found in more, №17886891, 09.04.2023 20:39

So, same answer is obtained in both the cases.

It is was helpful?

Faq

Mathematics
Step-by-step answer
P Answered by PhD

6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C

Step-by-step explanation:

To find:

6x^5(x^6-2)\,dx

Solution:

Method of substitution:

Let x^6-2=t

Differentiate both sides with respect to t

6x^5\,dx=dt

[use (x^n)'=nx^{n-1}]

So,

6x^5(x^6-2)\,dx = ∫ t\,dt = \frac{t^2}{2}+C_1 where C_1 is a variable.

(Use ∫t^n\,dt=\frac{t^{n+1} }{n+1} )

Put t=x^6-2

6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C_1

Use (a-b)^2=a^2+b^2-2ab

So,

6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C

where C=2+C_1

Without using substitution:

6x^5(x^6-2)\,dx = ∫6x^{11}-12x^5\,dx = \frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C

So, same answer is obtained in both the cases.

Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
Step-by-step answer
P Answered by PhD

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

Mathematics
Step-by-step answer
P Answered by PhD

The solution is given in the image below

The solution is given in the image below
Mathematics
Step-by-step answer
P Answered by PhD

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Try asking the Studen AI a question.

It will provide an instant answer!

FREE