Question

Suppose h is a function such that h(2) = −3, h'(2) = 3, h''(2) = 4, h(5) = 5, h'(5) = 6, h''(5) = 12, and h'' is continuous everywhere. Evaluate 5 h''(u) du.

Answer 1

Answer:

3

Step-by-step explanation:

It seems like your question is not complete.

So I will asume that it is like the one in the image.

But probably the answer is not 3 if the range is different from (1-2), eventhough, you just have to follow the same steps.

Answer 2

The value of $\int\limits^5_2 {h''(x)} \, dx$ if h'' is continuous everywhere is 3

The question is incomplete. The complete question asked us to find:

$\right. \int\limits^5_2 {h''(u)} \, du$

Given the following data from the question:

h(2) = −3,

h'(2) = 3

h''(2) = 4

h(5) = 5

h'(5) = 6

h''(5) = 12,

The given integral expression

$\int\limits^5_2 {h''(x)} \, dx =h'(5) -h'(2)$

Note that the integral of a second differential will give the first differential

From the given parameters:

$h'(5)=6 \\h'(2)=3$

Substitute into the integral expression:

$\int\limits^5_2 {h''(x)} \, dx =6-3\\\int\limits^5_2 {h''(x)} \, dx =3$

This shows that the value of $\int\limits^5_2 {h''(x)} \, dx$ if h'' is continuous everywhere is 3

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