For the functions ; compute

Formula of Integration by parts is:

Formula that makes connection between definite and indefinite integrals is (Fundamental theorem):

Gauss’s Formula:

Green’s formula:

If¶A is a set of all boundary points ofn A Í R , then a closure of A is

If3 f : [0,2p ]® R : t ® (cos t, sin t, t) and F(x, y, z) = (x, y, z), evaluate

If3 ] 2 , 0 [ : R ® p f : t ® (cos t, sin t, t) and f(x, y, z) = x + y + z. Evaluate integral line

If a curve C is given by the parametrical equations x=x(t), y=y(t), z=z(t), a< t <b, and f is real valued

function, then

If the curve is given by explicit equation, then its arc length =

If the curve is given by parametric equations, then its arc length =

If the curve is given by polar equations, then its arc length =

If x = r cos t cos u, y = r sin t cos u, z = r sin u, then Jacobean of this transformation =

If x = r cos t, y = r sin t, then Jacobean of this transformation =r

If x = r cos t, y = r sin t, z = z, then Jacobean of this transformation = r

Let F(x, y) = (3xy,-y2), and C denote the path of y = 2x2 from (1, 2) to (0, 0). Evaluate

Let F(x, y, z) = (2x – y + z, x + y - z2, 3x - 2y + 4z),and C denote the circle on the xy - plane with centre at the origin and radius 3, followed in the anticlockwise direction on the xy - plane.

Let for (un ≥ 0) the limit exist: then a) the series converges ifr <1; b) the series diverges ifr > 1; c) the test fails ifr = 1. The test is known as: Ratio test

Let for u (un ≥ 0) the limit exist: then a) the series converges ifr <1; b) the series diverges ifr > 1 ; c) the test fails ifr = 1. The test is known as: Root test

Let given two series: and If for any n: un ≤ vn , then a) from convergence of follows the convergence of The test is known as: Comparison test