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APMA 1110 Test Exam with
complete solutions latest version
∫1/√(x^2+4)
∫1/√(x^2-4)
∫1/(x^2+4)
∫1/(x^2-4)
∫1/√(4-x^2) - CORRECT ANSWER-1. trig sub x=2tanθ, dx=2sec^2θdθ
2. trig sub x=2secθ, dx=2tanθsecθdθ
3. integrate using one of the set up rules A/a tan^-1 x/a
4. decompose (factor completely)
5. trig sub x=2sinθ dx=2cosθdθ
∫1/√(x^2+4)
∫1/√(x^2-4)
∫1/(x^2+4)
∫1/(x^2-4)
∫1/√(4-x^2) - CORRECT ANSWER-1. trig sub x=2tanθ dx=2sec^2θdθ
2. trig sub x=2secθ dx=2tanθsecθdθ
3. integrate using the memorized formula A/a tan^-1 x/a
4. decompose
5. trig sub x=2sinθ dx=2cosθdθ
∫1/√(x+4)
∫1/√(x-4)
∫1/(x+4)
∫1/(x-4)
∫1/√(4-x) - CORRECT ANSWER-1. u-sub then integrate
2. u-sub then integrate
3. should know immediately (ln!)
4. should know immediately (ln!)
5. u-sub then integrate
∫x/√(x+4)
∫x/√(x-4)
∫x/(x+4)
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∫x/(x-4)
∫x/√(4-x) - CORRECT ANSWER-1. u-sub
2. u-sub
3. divide then integrate
4. divide then integrate
5. u-sub
∫x^2/√(x^2+4)
∫x^2/√(x^2-4)
∫x^2/(x^2+4)
∫x^2/(x^2-4)
∫x^2/√(4-x^2) - CORRECT ANSWER-1. trig sub x=2tanθ
2. trig sub x=2secθ
3. divide then integrate (or add and subtract 4)
4. divide then integrate (or add and subtract 4)
5. trig sub x=2sinθ
answer if the problem is set up as ∫A/(x+a)^n - CORRECT ANSWER-A/-(n-1)(x+a)^n-1
answer if the problem is set up as ∫A/x^2+a^2 - CORRECT ANSWER-A/a tan^-1 x/a
answer if the problem is set up as ∫A/x+a - CORRECT ANSWER-Aln|x+a|
answer if the problem is set up as ∫Ax/x^2+a - CORRECT ANSWER-A/2 x ln(x^2+a)
Anti-chain rule substitution.
What things do you make the u? - CORRECT ANSWER-Make the u:
- something raised to a power
- something inside a trig function
- power of e
- denominator of a fraction
Anti-power rule - CORRECT ANSWER-(cx^n+1)/n+1
antideriv of inverse sin - CORRECT ANSWER-xsin^-1x-∫x/(sqrt(1-x^2)
Antiderivative of e's and 1/x - CORRECT ANSWER-anti derivative of e is e
anti derivative of 1/x is ln|x|
Antiderivative of ln - CORRECT ANSWER-xlnx-x
Antiderivative trig functions - CORRECT ANSWER-anti derivative of cosx: sinx
anti derivative of sinx: -cosx
anti derivative of -sinx: -cosx
anti derivative of sec^2x: tanx
anti derivative of secxtanx: secx
anti derivative of csc^2x: -cotx
BRAINSCAPE1
APMA 1110 Test Exam with
complete solutions latest version
∫1/√(x^2+4)
∫1/√(x^2-4)
∫1/(x^2+4)
∫1/(x^2-4)
∫1/√(4-x^2) - CORRECT ANSWER-1. trig sub x=2tanθ, dx=2sec^2θdθ
2. trig sub x=2secθ, dx=2tanθsecθdθ
3. integrate using one of the set up rules A/a tan^-1 x/a
4. decompose (factor completely)
5. trig sub x=2sinθ dx=2cosθdθ
∫1/√(x^2+4)
∫1/√(x^2-4)
∫1/(x^2+4)
∫1/(x^2-4)
∫1/√(4-x^2) - CORRECT ANSWER-1. trig sub x=2tanθ dx=2sec^2θdθ
2. trig sub x=2secθ dx=2tanθsecθdθ
3. integrate using the memorized formula A/a tan^-1 x/a
4. decompose
5. trig sub x=2sinθ dx=2cosθdθ
∫1/√(x+4)
∫1/√(x-4)
∫1/(x+4)
∫1/(x-4)
∫1/√(4-x) - CORRECT ANSWER-1. u-sub then integrate
2. u-sub then integrate
3. should know immediately (ln!)
4. should know immediately (ln!)
5. u-sub then integrate
∫x/√(x+4)
∫x/√(x-4)
∫x/(x+4)
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, BRAINSCAPE1
∫x/(x-4)
∫x/√(4-x) - CORRECT ANSWER-1. u-sub
2. u-sub
3. divide then integrate
4. divide then integrate
5. u-sub
∫x^2/√(x^2+4)
∫x^2/√(x^2-4)
∫x^2/(x^2+4)
∫x^2/(x^2-4)
∫x^2/√(4-x^2) - CORRECT ANSWER-1. trig sub x=2tanθ
2. trig sub x=2secθ
3. divide then integrate (or add and subtract 4)
4. divide then integrate (or add and subtract 4)
5. trig sub x=2sinθ
answer if the problem is set up as ∫A/(x+a)^n - CORRECT ANSWER-A/-(n-1)(x+a)^n-1
answer if the problem is set up as ∫A/x^2+a^2 - CORRECT ANSWER-A/a tan^-1 x/a
answer if the problem is set up as ∫A/x+a - CORRECT ANSWER-Aln|x+a|
answer if the problem is set up as ∫Ax/x^2+a - CORRECT ANSWER-A/2 x ln(x^2+a)
Anti-chain rule substitution.
What things do you make the u? - CORRECT ANSWER-Make the u:
- something raised to a power
- something inside a trig function
- power of e
- denominator of a fraction
Anti-power rule - CORRECT ANSWER-(cx^n+1)/n+1
antideriv of inverse sin - CORRECT ANSWER-xsin^-1x-∫x/(sqrt(1-x^2)
Antiderivative of e's and 1/x - CORRECT ANSWER-anti derivative of e is e
anti derivative of 1/x is ln|x|
Antiderivative of ln - CORRECT ANSWER-xlnx-x
Antiderivative trig functions - CORRECT ANSWER-anti derivative of cosx: sinx
anti derivative of sinx: -cosx
anti derivative of -sinx: -cosx
anti derivative of sec^2x: tanx
anti derivative of secxtanx: secx
anti derivative of csc^2x: -cotx
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