Let f(t)= F"(t), with F(t) = 5t2 +t, and let a = 4 and b=7. Write the integral f f(t) dt and evaluate it using the Fundamental Theorem of Calculus. Ja dt = 1. 1. 1. =

Q: e™ +1 4 (Fund. Thm. of Calculus) Find F'(x) if F(x) = S (In(t – 1))2018 dt

A: Given:                   F(x)=∫xex+1ln(t-1)2018 dt To determine:                 F'(x)=?   Solution:…

Q: Assume that f and g are harmonic functions in R^n. Show that div(f ∇g − g∇f ) = 0.

A: Ans- We can start by computing the divergence of the vector field F = f∇g - g∇f:

Q: Suppose v(t) gives a particle's velocity at time t , in miles per hour. Write an integral expression…

A: Let the particle velocity v(t) at time t , (in miles per hour)

Q: Differentiate. 7t f(t) t3 - t - 1 f'(t) =

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Q: Find derivative of this integral, here Br is a brownian motion

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Q: Let y = xbex (where b is a real number). Determine y'.   Let y = (3x + 6)/(6x + 12). Determine y'.

A: given y=xbex to find the derivative y' use the product rule uv'=uv'+vu' therefore,…

Q: Differentiate the following function.   r(t)=(t e^-t,5tln t,t sin t)

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Q: et f(z) = | t'dt. Evaluate the following.

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Q: 2 DiFferentiate JE F(E) = Sépsx swx + Jbx SK Sinxt XHI と

A: Differentiate Ft=∫t2tcosxsinx+1x+1dx