Question

6) Find the Antiderivative of sec(x) tan(x)dx- if you found an antiderivative for this explain why the result for the definite integral using the same function is undefined??

 

7) Given the function h(x)= (square root of x)*ln(sin(x))--> Use a calculator to evaluate each of the following and round to the nearest thousandth (3 decimal places).

**Given--> h(x)= (square root of x)*ln(sin(x))

a) The integral from 0.5 to 3 h(x)dx

 

b)The integral from 3 to 2 h(x)dx

 

 

c)The integral from 7 to 9 |h(x)| dx

Answer 1

6.

$\int\sec x \tan x dx=\int\frac{1}{\cos x}.\frac{\sin x}{\cos x}dx\\$

Let $u=\cos x, du=-\sin xdx.$

$-\int\frac{1}{u^2}du=\frac{1}{u}+C=\frac{1}{\cos x}+C= \sec x+C.$

There is no definite integral in the question to check whether it is undefined.

7. Using wolfram alpha calculator

(a) $\int_{0.5}^3 h(x)=1.2999 ≈1.300$

(b) $\int_3^2h(x)=1.07883 ≈1.079$

(c) $\int_7^9h(x)=1.17709≈1.177$