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Integrate xsin(x) by parts between the limits of -pi/2 and +pi/2

Let u = x and dv/dx = sin(x),

By using the general expression of:

integral(u multiply dv/dx)dx = [u multiply v] - integral(v multiply du/dx)dx, and by realising that:

Answered by Matthew B. • Maths tutor

3356 Views

Differentiate x^2+6x+1

All we do here is break down into three parts: x², 6x & 1.x² becomes 2x as we multiply by the power and then decrease the power by one.6x becomes 6 and 1 becomes 0.So alltogether...

Answered by Samuel I. • Maths tutor

4132 Views

find the definite integral between limits 1 and 2 of (4x^3+1)/(x^4+x) with respect to x

first notice the integral is in the form f'(x)/f(x), and indefinite integrals of this form are ln|f(x)|+c.
therefore the integral is [ln|x⁴+x|] between limits 1 and 2.
subbing in li...

Answered by Tutor22645 D. • Maths tutor

4175 Views

Form the differential equation representing the family of curves x = my , where, m is arbitrary constant.

Differentiating the above equation with respet to y:dx/dy = m;Substituting the value of m in the given form:x = (dx/dy) y i.e. the solution is(dx/dy) y - x = 0

Answered by Piyush S. • Maths tutor

7782 Views

Find the positive value of x such that log (x) 64 = 2

Find the positive value of x such that log_x64 = 2
Using the logarithm rules, we know that we can rearrange the given equation into the form:
x² = 64
Knowing this, we s...

Answered by Santiago G. • Maths tutor

17699 Views