With the help of trapezoidal rule for numerical integration and the following table.

Question

With the help of trapezoidal rule for numerical integration and the following table. (A)  0.35342  (B)  0.34375  (C)  0.34457  (D)  0.33334

Tardigrade Admin · Accepted Answer

We know, the trapezoidal rule is ∫abf(x)dx =(h/2)[(y0+yn)+2(y1+y2+...+yn)] But, we have a=0, b=1, h=0.25, n=5 ∴ ∫abf(x)dx =(0.25/2)[(0.1+2(0.0625+0.25+0.5625)] =(0.25/2)[1+1.75] =0.34375

Q. With the help of trapezoidal rule for numerical integration and the following table.

$0.35342$

$0.34375$

$0.34457$

$0.33334$

We know, the trapezoidal rule is
$\int_{a}^{b} f (x) d x$
$= \frac{h}{2} [(y_{0} + y_{n}) + 2 (y_{1} + y_{2} + ... + y_{n})]$
But, we have $a = 0, b = 1, h = 0.25, n = 5$
$∴$ $\int_{a}^{b} f (x) d x$
$= \frac{0.25}{2} [(0.1 + 2 (0.0625 + 0.25 + 0.5625)]$
$= \frac{0.25}{2} [1 + 1.75]$
$= 0.34375$

Q. With the help of trapezoidal rule for numerical integration and the following table.

0.35342

0.34375

0.34457

0.33334

We know, the trapezoidal rule is ∫ab​f(x)dx =2h​[(y0​+yn​)+2(y1​+y2​+...+yn​)] But, we have a=0,b=1,h=0.25,n=5 ∴ ∫ab​f(x)dx =20.25​[(0.1+2(0.0625+0.25+0.5625)] =20.25​[1+1.75] =0.34375

$0.35342$

$0.34375$

$0.34457$

$0.33334$

We know, the trapezoidal rule is
$\int_{a}^{b} f (x) d x$
$= \frac{h}{2} [(y_{0} + y_{n}) + 2 (y_{1} + y_{2} + ... + y_{n})]$
But, we have $a = 0, b = 1, h = 0.25, n = 5$
$∴$ $\int_{a}^{b} f (x) d x$
$= \frac{0.25}{2} [(0.1 + 2 (0.0625 + 0.25 + 0.5625)]$
$= \frac{0.25}{2} [1 + 1.75]$
$= 0.34375$