Final answer to the problem
$8.1\times 10^{-4}\left(-5\left(-0.25\cdot e^{-35}\cos\left(140\pi \right)+0.25\cdot e^{-7}\right)-19.6349541\cdot e^{-35}\sin\left(140\pi \right)\right)$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
Simplify the expression
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$\int_{0}^{7}-5e^{\left(-4t-7\right)}\cos\left(20\pi t\right)dt$
Learn how to solve problems step by step online. Integrate the function -5e^(-5t)cos(20*pit)e^(t-7) from 0 to 7. Simplify the expression. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. We can solve the integral \int e^{\left(-4t-7\right)}\cos\left(20\pi t\right)dt by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du.
Final answer to the problem
$8.1\times 10^{-4}\left(-5\left(-0.25\cdot e^{-35}\cos\left(140\pi \right)+0.25\cdot e^{-7}\right)-19.6349541\cdot e^{-35}\sin\left(140\pi \right)\right)$
