The Area Of The Inner Cross-Section

ENGINEERING MATHEMATICS
Problem 1
Width of the rectangles= b−a
n
2−0
4
=0.5
Upper sum:
Area ≈A1 + A2 +A3 +A4
≈f(x1)∆X +f(x2)∆ x +f(x3)∆ x +f(x4)∆ x
≈f(1)∆x + f(2)∆ x +f(3)∆ x +f(4)∆ x
≈1*0.5 +0.7*0.5 +0.5*0.5 +0.4 *0.5
≈1.3 squared units
0 0.5 1 1.5 2 2.5 3
0
0.2
0.4
0.6
0.8
1
1.2
1
0.7
0.5
0.4
0.3 0.3
f(x) = exp( − 0.56 x )
R² = 0.98
y
y
Exponential (y)
x-axis
y-axis

Lower sum:
0 0.5 1 1.5 2 2.5 3
0
0.2
0.4
0.6
0.8
1
1.2
y
Exponential (y)
x1
x2
Linear (x2)
x3
Linear (x3)
Linear (x3)
x4
Area ≈A1 + A2 +A3 +A4
≈f(x1)∆X +f(x2)∆ x +f(x3)∆ x +f(x4)∆ x
≈f(1)∆x + f(2)∆ x +f(3)∆ x +f(4)∆ x
≈0.7* 0.5 +0.5*0.5 +0.4*0.5 +0.3 *0.5
≈0.95
Problem 2
If the curve y= 6xe-x^2
Area =∫
0
2
6 x e− ( x2 )
¿ ¿
=6 ∫
0
2
x e−x2
¿ ¿dx
6[v.du]20
=6[1. e−¿x3
x3 ¿ +c]