Evaluate the definite integral a ∫−2x√(x^2+a^2) dx -a

Evaluate the definite integral a ∫−2x√(x^2+a^2) dx -a

Evaluate I =⌠⌠FdS , where F( x,y,z) = x^3 i + y^3 j + z^3 and S is the surface of the solid bounded by the hemisphere z =sqrt(1-x^2-y^2)and the plane z = 0

F=e^y i+(xe^y+e^z)j + (ye^z)k evaluate ⌠Fdr along A(0,2,0) and B(4,0,3). Find if its conservative and if so find its potential then use A and B.

Helium is pumped into a spherical balloon at a rate of 5 cubic feet per second. How fast is the radius increasing after 2 minutes? Rate of change of radius (in feet per second)...

Evaluate the given indefinite integrals. a) ∫ a dx=_____+C b) ∫ t^2 dx=_______+C

Evaluate the definite integral (if it exists) 2 ∫ −1x(√x-1) dx 1

List the critical numbers of the following function in increasing order. Enter N in any blank that you don't need to use. G(x)=^3√3x^2-3x The square root is over everyt...

Let \displaystyle g(x)=\int_0^x {\sqrt{1+6 t}}\,dt. Use the Fundamental Theorem of Calculus to find g'(x).

Evaluate the definite integral 1 ∫ x^2√(4x+8x) dx 0

If f(x)=1x+2, find f′(−5), using the definition of derivative. f′(−5) is the limit as x→_____ of the expression __________ The value of this limit is _________

Use Newton's method to approximate the indicated root of the following equation correct to six decimal places. The root of 2x^3−6x^2+3x+1=0in the interval [2,3].

Find dy/dx in terms of x and y if ^4√x=3√y. dy/dx=_____

Find the absolute maximum and absolute minimum values of the function f(x)=x^3−12x^2−27x+10 over each of the indicated intervals. a) Interval [-2,0] 1. Absolute max= 2...

g(x)=∫ (x on top, 0 on bottom) √(1+6t) dt, use fundamental theorem of calculus find g1(x) (derivative of g(x). )

The top of a 17 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 4 feet per second. How fast is the bottom of the ladder sliding along the ground when the bottom...

Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 9 mi^2/hr. How rapidly is radius of the spill increasing when the area is 9 mi^2?

Find the derivative of w=(√t+5)^76 dw/dt=______

Find the derivative of f(x)=√[6−sinx/2−cosx] The square root is over everything. f'(x)=____

For the function f(x)= {x^2−4, 0≤x<3 f(x)= {−1, x=3 f(x)= {3x-4, 3 less than x use algebra to find each of the following limits: lim f(x)= x→3^+ lim...

If ∫ (7 on top, 1 on bottom) f(z)dx= 16 and ∫ (7 on top, 6 on bottom) f(x) dx= 3.3, find ∫ (6 on top, 1 on bottom) f (x) dx

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