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solve the following definite integral by decomposition into partial fractions: \int_{1}^{2}{\frac{1}{x^2+x}}dx

\frac{1}{x^2+x}=\frac{A}{x} + \frac{B}{x+1}, 1=A(x+1)+Bx, let x=-1: 1=-B, B=-1let x=0: 1=A, A=1Hence, \int_{1}^{2}{\frac{1}{x^2+x}dx} = \int_{1}^{2}{\frac{1}{x}dx} - \int_{1}^{2}{\frac{1}{x+1}dx}=[ln(x)-l...

Answered by Maths tutor
3139 Views

How can I best prepare for the essay segment of the exam?

The essay is usually either a discursive or an argumentative essay. Because of this, it is best to be prepared for both possibilities; however, the discursive essay is arguably more difficult since you ha...

DB
Answered by Dávid B. LNAT tutor
1210 Views

Consider the function y = x.sin(x); differentiate the function with respect to x

Using the product rule :u = x, so du/dx = 1
v = sin(x), so dv/dx = cos(x)
Therefore dy/dx = v(du/dx) + u(dv/dx) So dy/dx = sin(x) + x.cos(x)

BR
Answered by Ben R. Maths tutor
3924 Views

In the poetry of Sylvia Plath do the women and their relationships challenge or reinforce gender stereotypes?

Through the lens of a feminist critic, there are a great many ways in which to interpret the poetry of Sylvia Plath. In the poem ‘Spinster’ Plath presents a narrator who rejects her suitors, inst...

EM
10800 Views

The UK government are planning on imposing a tax on sugary drinks. Discuss how a tax could be used to decrease consumption of sugary drinks and outline some potential issues.

Gov should try place monetary value on welfare loss - this may be difficult tax would increase cost of production for firms - they supply less (shown on supply and demand diagram)tax would deter customers...

AA
Answered by Ahmad A. Economics tutor
1295 Views

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