trapezoidal rule

What is the number of trapeziums if there are 6 ordinates?

• 6

• 7

• 5

• 4

What is the increment in x-ordinate for  $\int_1^6x^2\sqrt{\sin x+1}dx$  with 6 ordinates?

• 0.5

• 1

• 0.2

• 5/6

Using the trapezoidal rule will yield the following results except

• The answer is just an approximation

• The answer is over-estimated

• The answer is under-estimated

• The answer is not an exact answer

Approximate the area under the curve over the given interval using 4 trapezoids.

• A

• B

• C

• D

Approximate the area under the curve over the given interval using 4 trapezoids.

• A

• B

• C

• D

The approximate value for  $\int_0^1\sqrt{1+x^2}dx$  with 5 strips is

• 1.25

• 1.05

• 1.15

• 1.35

The width of the trapezoid of the definite integral   $\int_{0.5}^1e^{x^2}dx$  with with 5 ordinates is 

• 0.1

• 0.3

• 0.125

• 0.375

Give your answer in 4 significant figures

• 1.463

• 1.464

• 1.512

• 1.518

The correct formula for Trapezoidal Rule  of the definite integral  $\int_a^bydx$  , where  $y=f\left(x\right)$   is

•  $\frac{b-a}{n}\left[y_0+y_n+2\left(y_1+y_2+...+y_{n-1}\right)\right]$  

•  $\frac{b-a}{2n}\left[y_0+y_n+y_1+y_2+...+y_{n-1}\right]$  

•  $\frac{b-a}{2n}\left[y_0+y_n+2\left(y_1+y_2+...y_{n-1}\right)\right]$  

•  $\frac{b-a}{n}\left[y_0+y_n+\left(y_1+y_2+...+y_{n-1}\right)\right]$  

Which of the followings statement is FALSE.

• 8 strips , n = 8

• 6 sub interval, n = 6

• 7 ordintes , n = 7

• 10 interval, n = 10