Find the arc length of the curve y = In(cos(x)) , 0 < x < - In(3v3) O a. O b. In(v3) O In(v3 + 1) Od In(3v3 + 1)

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Q: [1] S(4x³ + x)V4x² + 1dx > [2] S(2x7/2 – vx)* d. [3] S V1+ 2sin3xcos3xdx

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Q: %3D 8. Use the Intermediate Value Theorem to prove that the equation e~² + x² = 4 has a real root.

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Q: Compute In = x² sin(x) dx for n = 2, 4, 10, 20, 50, and 100 using Newton-Cotes quadrature.

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Q: Find the arclength of y = 2x/2 3/2 on 1 < x < 3

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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.