# Method of Integration, Identity Matrix, Differential Equation, and Linear Equations (Math Problem Sample)

This technical paper entails solving five calculus problems. The first problem required me to integrate xsin 3x with respect to x. Using the method of integration by parts, I managed to get the solution as = 1/9sin 3x-1/3xcos 3x+C.

The second question required the determination of the value of α in an identity matrix expressed in a trigonometric form. The value of α was found to be 0.

We are given two equations in the third question, where we are required to determine the value of m. Here, we need to understand the principles of linear equations in a Cartesian plane.

The fifth question has three linear equations where I was required to solve for x and y using the matrix method.

Student’s Name

Professor Name

Course

Date

Calculus

Question 1:

To evaluate ʃ x sin 3x dx, we use the method of integration by parts given by the formula;

ʃ u dv = uv-ʃ v du

Let u = x, dv = sin 3x; then, v= -cos 3x and du = dx. Now substituting in the formula we get;

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