True or False? 1.Numerical integration techniques can be used to approximate a d

Question

True or False?

1.Numerical integration techniques can be used to approximate a definite integral as long as the error is acceptably small.

2.The area of a trapezoid is one-half the height times the sum of the bases (parallel sides)

3. A larger n generally reduces the error in using numerical integration, however a larger n potentially increase the round-off errors in calculation.

4. When calculating the area between two curves, if the curves intersect you must find all intersection points, then subdivide the interval of integration and adjust the integrand accordingly so that the proper function is always on top.

5.It may be impossible to find the antiderivative of f(x) in terms of elementary functions.

6.The Trapezoidal Rule and Simpson’s Rule are both examples of numerical integration techniques.

Explanation / Answer

1.Numerical integration techniques can be used to approximate a definite integral as long as the error is acceptably small.
True
If error is small, numerical integration can be considered approximation for definite integral

2.The area of a trapezoid is one-half the height times the sum of the bases (parallel sides)
True
A = 0.5*(B1+B2)*H

3. A larger n generally reduces the error in using numerical integration, however a larger n potentially increase the round-off errors in calculation.
True

4. When calculating the area between two curves, if the curves intersect you must find all intersection points, then subdivide the interval of integration and adjust the integrand accordingly so that the proper function is always on top.
True
we need to calculate area between curve for all points and then add them

5.It may be impossible to find the antiderivative of f(x) in terms of elementary functions.
True
Sometimes function may be complex

6.The Trapezoidal Rule and Simpson’s Rule are both examples of numerical integration techniques.
True

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