Expert: Ahmed Salami - 5/10/2009

Question
need to evaluate the integral using T-Rule

e ^ x^2 .dx with lower limit 1 and upper limit 2
and n=10  

Answer
Hi Farooq,
To find the definite integral (Area) of a function between the limits a and b using the trapezoidal rule,
A = d[y0/2 + y1 + y2 + ......... + y(n)/2]
where d = (b-a)/n
and the y's are the values at intermediate values at intervals of d.
For y = e^(x^2) from the limits 1 to 2
d = (2-1)/10 = 0.1
The x values are then 1, 1.1, 1.2, ...... , 2
y0 = e^(1^2) = 2.7183
y1 = e^(1.1^2) = 3.3535
y2 = e^(1.2^2) = 4.2207
y3 = e^(1.3^2) = 5.4195
y4 = e^(1.4^2) = 7.0993
y5 = e^(1.5^2) = 9.4877
y6 = e^(1.6^2) = 12.9358
y7 = e^(1.7^2) = 17.9933
y8 = e^(1.8^2) = 25.5337
y9 = e^(1.9^2) = 36.9661
y10 = e^(2^2) = 54.9482
Therefore,
A = (0.1)[2.7183/2 + 3.3535 + 4.2207 + ......... + 54.9482/2]
 = 15.18 sq units

Regards