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Integration

The document outlines various integration formulas and techniques, including basic integration rules for polynomials, constants, exponential, and trigonometric functions. It also explains how to compute definite integrals and find the area under a curve using integration. Examples are provided to illustrate the application of these formulas.

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thet.htarsan087
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6 views3 pages

Integration

The document outlines various integration formulas and techniques, including basic integration rules for polynomials, constants, exponential, and trigonometric functions. It also explains how to compute definite integrals and find the area under a curve using integration. Examples are provided to illustrate the application of these formulas.

Uploaded by

thet.htarsan087
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Integration Formula

𝑦= 𝑓 (𝑥). 𝑑𝑥

𝑥
1. 𝑥 𝑑𝑥 = +𝑐
𝑛+1

Eg. ∫ 𝑥 𝑑𝑥 = +𝑐

Eg. ∫ 2𝑥 𝑑𝑥 = +𝑐

2. (𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡) 𝑑𝑥 = (𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)𝑥 + 𝑐
Eg. ∫ 3 𝑑𝑥 = 3𝑥 + 𝑐

(𝑎𝑥 + 𝑏)
3. (𝑎𝑥 + 𝑏) 𝑑𝑥 = +𝑐
(𝑛 + 1)𝑎
( )
Eg. ∫(2𝑥 + 3) 𝑑𝑥 =
∗

𝑒
4. 𝑒 𝑑𝑥 = 𝑒 + 𝑐 , 𝑒 𝑑𝑥 = +𝑐
𝑎

cos(𝑎𝑥 + 𝑏)
5. sin 𝑥 𝑑𝑥 = − cos 𝑥 + 𝑐 , sin(𝑎𝑥 + 𝑏) 𝑑𝑥 = − +𝑐
𝑎

sin (𝑎𝑥 + 𝑏)
6. cos 𝑥 𝑑𝑥 = sin 𝑥 + 𝑐 , cos(𝑎𝑥 + 𝑏) 𝑑𝑥 = +𝑐
𝑎

1 1 ln(𝑎𝑥 + 𝑏)
7. 𝑑𝑥 = ln 𝑥 + 𝑐 , 𝑑𝑥 = +𝑐
𝑥 𝑎𝑥 + 𝑏 𝑎

1
Integration with limit

𝒃
𝒇(𝒙) 𝒅𝒙 = [𝒇(𝒙)]𝒃𝒂 = 𝒇(𝒃) − 𝒇(𝒂)
𝒂

Eg. ∫ 4𝑥 + 3𝑥 + 4 𝑑𝑥

=[ + + 4𝑥 ]

∗( ) ∗( ) ∗( ) ∗( )
=[ + + 4(2)] - [ + + 4(1)]

= -

=50

2
Area Under Curve

Area = ∫ 𝑓(𝑥) 𝑑𝑥
F(x)

x
a b

y
𝑦

Area = ∫ (𝑦 − 𝑦 ) 𝑑𝑥
𝑦

x
a b

y
𝑦

Area = ∫ (𝑦 − 𝑦 ) 𝑑𝑥
𝑦

x
a b

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