2. Find (in terms of t): x = 2 + 3 sin t y = -1+4 cos t

Q: Let csct = V5,t e QII Find sin(2t) 4 O 2 V5 V5 25

A:

Q: Evaluate [sin³ a x cos x dx. + C

A:

Q: Convert r = 6(sin(0) + cos(0)) to an equation in rectangular coordinates in terms of x and y.

A:

Q: 7. Compute •+∞ COS X x¹ + x² + 1 -dx.

A:

Q: 5. Use substitution to find S sin1º0 cos 0 d0.

A: We will find the integration.

Q: 1. (a) Evaluate: f sin?r cos'r dr. (b) Evaluate: (2 – |2|) dr.

A: Answer and explanation is given below...

Q: Find the W (sinx,cosx , sec x).

A:

Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

A:

Q: For F(t) = (3 cost, 3 sin t, 4t) find T,Ñ, and B

A: Given that : r→(t)=3cost,3sint,4t. Therefore, r'(t)=-3sint,3cost,4. So, r'(t)=9+16=5. Therefore,…

Q: Q57.a) Find if y=sin(tant) and t=cos(x) dx

A:

Q: (tanxaa

A:

Q: 2 Cos4 Sin (sinz) de

A: Consider the integral  ∫cosxsin2sinxdx

Q: Solve for the convolution of sin (t) and cos (t).

A:

Q: (2 sin r - e) dr.

A:

Q: Evaluate: D°(sin x- e20) A -sin x - 32e* B sin x - 32e2 © -32- e D cos x - 32e2

A:

Q: • Evaluate y cos (r") dæ dy

A:

Q: 2. Evaluate each. (a) sin(y²) dy dr cln(2) -In(5) e2z+y dy dx (b)

A: We use change in order of part a

Q: can

A: We have to find the value of: sin tan-1 38

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.