zow(t)dt = zo / w(t)dt. 2. a. [w(t) + W(t)]dt = | w(t)dt + | w(t)dt 3.

Q: (n) If g(x) = o f(t) dt, then g(2)

A: We plug x=2 in the given function

Q: Consider the function I(7) defined by: 1 I(7) = Jo -t/T dt What is 4?

A: Given function is  Iτ=1τ∫0∞e−t/τ To find dIdτ

Q: ds/dt if s=(t9+6)(t8-6)

A:

Q: The set of functions {Vx, x, x²} is linearly dependent on (0, oo). True False

A:

Q: If fo f(t)dt = 2, So f(t)dt = -6, and f(t)dt = 1, find i f(t)dt.

A:

Q: 1 X ƒ (t) dt = 1 – 1 418

A: Given:  ∫1xft dt=1-1x To Find:  To find ft.

Q: Let dx dt x(t): = 3et 2. Find x(t) such that x(0) = 2.

A:

Q: (a) Let v(t) be a differentiable vector valued function of t. If v. (dv/dt) = 0 for all t, can we…

A: The objective of the question is to determine if we can say anything about the magnitude of a vector…

Q: Find a function f that satisfies the equation | f(t) dt = 2 cos x + 3x – 2. %3D -

A: Derivative of a definite integral is: ddx∫0xf(t)dt=f(x) Formulae used: ddxcosx=-sinxddxx=1ddxC=0…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.