List of useful integrals
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Integral of a polynomial function:
If \(x(t)=At^n \Longrightarrow \int_{t_{i}}^{t_{f}} x(t)dt=\frac{A}{n+1}(t_{f}^{n+1}-t_{i}^{n+1}) \)
where \(A\) and \(n\) are constants.
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Integral of an exponential function:
If \(x(t)=A e^{bt}\Longrightarrow \int_{t_{i}}^{t_{f}} x(t)dt=\frac{A}{b}(e^{bt_{f}}-e^{bt_{i}}) \)
where \(A\) and \(b\) are constants.
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Integral of \(1/t\):
If \(x(t)=\frac{1}{t} \Longrightarrow \int_{t_{i}}^{t_{f}} x(t)dt=\ln(t_{f})-\ln(t_{i})=\ln(\frac{t_{f}}{t_{i}}) \)
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Integral of sine:
If \(x(t)=A\sin(b+ct) \Longrightarrow \int x(t)dt=-\frac{A}{c}\cos(b+ct) + D \)
where \(A\), \(b\) and \(c\) are constants, and \(D\) is an integration constant.
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Integral of cosine:
If \(x(t)=A\cos(b+ct) \Longrightarrow \int x(t)dt=\frac{A}{c} \sin(b+ct) + D \)
where \(A\), \(b\) and \(c\) are constants, and \(D\) is an integration constant.
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