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Differentiate y=(x^2+1)(e^-x)

Here, we're using the product rule (and the chain rule for the e -x ): y=(x 2 +1)(e -x ) dy/dx=(2x)(e -x )+(x 2 +1)(-1)(e -x ) Then we simplify to get: dy/dx=(e -x )(2x-x 2 -1)
RD
Answered by Rishav D. • Maths tutor
7446 Views

Integrate the following function: f(x) = 8x^3 + 1/x + 5

We can see that the function is a sum of three terms so we can deal with each term separately and add them up. The term 8x 3 and 5 are relatively straightforward and follow the standard rules for integration...
EJ
Answered by Eleanor J. • Maths tutor
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Using the substitution of u=6x+5 find the value of the area under the curve f(x)=(2x-3)(6x+%)^1/2 bounded between x=1 and x=1/2 to 4 decimal places.

dx=du/6 => (u-5)/6=x So the integral is now (2((u-5)/6)-3)(u^1/2) du/6 Which through simplifying becomes (1/36)(2u-28)(u^1/2)du = (1/36)(2u^3/2 -28u^1/2)du After integrating becomes (1/36)(4(u^5/2)/5 -56(...
JT
Answered by Joseph T. • Maths tutor
4488 Views

What is the best way to revise for a Maths A-level?

The best method to revise is through solving past questions and timed exam papers. As long as you have your notes and understand all the basic principles, then you just need to practice in order to avoid get...
AE
Answered by Ayah E. • Maths tutor
8905 Views

Integration by parts: Integrate the expression x.ln(x) between 1 and 2.

Let $ denote the integral symbol, as I am limited here by my keyboard. Recall the formula for integration by parts: $ u.(dv/dx) dx = uv - $ u(dv/dx) dx So to find $ pi 0 x.sin(x) dx, we must allocate x and s...
RH
Answered by Rebecca H. • Maths tutor
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