dy/dx = 8(8x - 5)(4x² - 5x )^ 7
differentiate using the ' chain rule '
dy/dx = 8(4x² - 5x)^ 7 × d/dx (4x² - 5x)
= 8(4x² - 5x)^ 7 × (8x - 5)
= 8(8x - 5)(4x² - 5x)
The limit as a definite integral on the interval
on [2π , 4π] is
.
<h3>
What is meant by definite integral?</h3>
A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.
Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.
If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.
Let the equation be

substitute the values in the above equation, we get
=
on [2π, 4π],
simplifying the above equation

To learn more about definite integral refer to:
brainly.com/question/24353968
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Answer:
B
Step-by-step explanation:
All we have to do is plug in the values! 1/2(4)(10+5) will give us the area. Now we simplify!
2(15) = A
30=A
Our answer is B!
B, 2 5/8.
2 and 5/8 times itself is 5 1/4, meaning its half of 5 1/4.
1. The answer is 16^2, so B.
16 x 16 = 256
2. The answer is 17, so B.
Some of the factor of 68 are: 1, 2, 4, 17, 34 and 68.
3. The answer is 15, so B.
Only 15 is composite since it contains more than a factor, which are 3 and 5. The rest of the numbers are prime since they only contain a factor.
4. The answer is 2^2^3^7, so B.
The factor tree:
84
2 x 42
2 x 2 x 21
2 x 2 x 3 x 7
Hope this helps! :)