Chapter 7.5, Problem 3QR

To determine

To find: The value of definite integral bye use the anti derivative.

Answer to Problem 3QR

The answer is: $\frac{\sqrt{2}}{2}$

Explanation of Solution

Given information:

The integral is:

Calculation:

It is well-known that antiderivative of the function $\sin (x)$ is the function $-\cos (x)$ So that, to calculate the integral

  

Only need to apply the Calculus Fundamental Theorem.

The integral can be calculated as follows using the Fundamental Theorem of Calculus:

  

Therefore, the required the value of definite integral bye use the anti derivative is $\frac{\sqrt{2}}{2}$ .

$\text{(b)}$

To determine

To find: The value of definite integral by use NINT.

Answer to Problem 3QR

The answer is: $0.7071067811865$

Explanation of Solution

Given information:

The integral is:

Calculation:

To use NINT and obtain the value of the given integral is approximately equal to:

  $NINT\left(\sin (x),x,\frac{\pi }{4},\frac{\pi }{2}\right)\approx 0.7071067811865$

Therefore, the required value of definite integral by use NINT is $0.7071067811865$ .