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Title: INTEGRATION LECTURE NOTES
Description: WELL DETAILED CLASS NOTES ON INTEGRATION WITH SASAMPLE QUESTIONS
Description: WELL DETAILED CLASS NOTES ON INTEGRATION WITH SASAMPLE QUESTIONS
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INTEGRATION LECTURE NOTES
INTEGRATION
Standard integrals
Examples:
d/dx ( -cos x)=sin x
d/dx (ex)=ex + c
power rule for integration
ʃ2x3 dx = x4/2 +c
ʃ x3/5 dx = x8/5/(8/5) + c
constant multiple rule and sum rule for any constant
ʃ c(f(x)) = c ʃ f(x)
The integral of a constant times a function is equal to the constant times
the integral of the function
...
5x2 +sin x dx
solution:
3ʃex dx + 2(1/x)dx + 0
...
The definite integral of f(x) from a to b
is the difference
...
The product rule differentiation is given as:
d(uv)/dx = udv/dx + vdu/dx
integrate both sides:
uv=ʃ udv/dx + ʃ vdu/dx
ʃudv= uv- ʃvdu
where dv is the derivative of v and du is the derivative of u
...
dv= x2
u= In x dx
v= x3/3
du= 1/x
INTEGRATION LECTURE NOTES
ʃudv =uv-ʃvdu
ʃ x2 In x dx – In x(x3/3) - ʃ x3/3(1/x)
x3/3In x dx - ʃx2/3 dx
[x3/3In x- x3/9]
x3/3[In x – 1/3]+ c
Title: INTEGRATION LECTURE NOTES
Description: WELL DETAILED CLASS NOTES ON INTEGRATION WITH SASAMPLE QUESTIONS
Description: WELL DETAILED CLASS NOTES ON INTEGRATION WITH SASAMPLE QUESTIONS