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How can I remember when a turning point of a function is a maximum or a minimum?

The key is to look at the first and second derivatives of that function. Remember that a turning point always has the first derivative equal to zero. Then, the sign of the second derivative indicates if that...
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Answered by Titus D. • Maths tutor
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Using the substitution x = 2cosu, find the integral of dx/((x^2)(4-x^2)^1/2), evaluated between x=1 and x=sqrt(2).

Starting with x=2cosu, rearrange for u to get u=arccos(x/2), then find the upper and lower limits of the integral. We find that our lower limit goes from 1 to pi/3, ad our upper limit goes from root 2 to pi/...
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Answered by Tayn D. • Maths tutor
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Calculate the integral of e^x*sin x

1/2 *e^(x)(sin x -cos x)
Answered by • Maths tutor
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integrate arcsin(x)

Use integration by parts to obtain:u=arcsin(x), u'=1/(1-x 2 ) 0.5 , and v'=1, v=x Using the equation: integral of uv' = uv - integral of u'vintegral of arcsin(x) = xarcsin(x) - integral of x/(1-x 2 ) 0.5 Use...
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Answered by Maya G. • Maths tutor
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The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5 Work out the area of the triangle.

72 / (3+4+5) = 6base :3 6 = 18height :4 6 = 24area = (base * height) /2area = (18*24)/2=216 cm ^2
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Answered by Ibrahim H. • Maths tutor
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