Maths Integration

Maths integration

Contents
Contents...........................................................................................................................................2
MAIN BODY..................................................................................................................................1

MAIN BODY
1. The values of 𝑦, for a curve with equation 𝑦=𝑓(𝑥),have been tabulated below.
x 1 2.25 3.5 4.75 6
y 9 17 25 21 13
Use the trapezium rule with all the values from the above table to find an estimate
for the integral.
Solution: As per the formula which is as follows:
Area= 1/2 h[y0+2(y1+y2+_____+yn-1)+yn]
Where, h= b-a/n
Here we have, h= 6-1/4 = 5/4
Putting in the values we have,
=1/2 (5/4) [9+2(17+25+21)+13]
=5/8*148
=185/2
=92.5
2. Find a general expression for 𝑦 given that

Solution: dy/dx= 4x+3
dy=(4x+3)dx
∫dy= 4∫xdx+ 3∫dx
y= 4x2 /2 + 3x
=2x2 + 3x
3. Find
(a) ∫(2𝑥+4)𝑑𝑥
Solution: ∫ (2x+4)dx
=2∫xdx+ 4∫dx
=2x2/2+ 4x
= x2+ 4x
(b)
Solution:
= ∫ 2x2+x-1/2x5 *dx
= ∫ 2x2/2x5*dx + ∫ x/2x5*dx - ∫ 1/2x5*dx
=x-2/-2 +1/2*x-3/-3 – ½*x-4/-4
= -1/2x3- 1/6x3+ 1/8x4
=1/8x4 – 1/6x3 – 1/2x2