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What is the indefinite integral of xlog(x)?

The integral can be split into two different functions of x which is a hint that we must use the integration by parts method. The method is defined as ∫ uv’ dx = uv - ∫ u’v dx . If we let u = log(x) and v’ =...
WH
Answered by William H. • Maths tutor
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Using the binomial theorem, find the coefficient of x^4*y^5 in (x-2y)^9.

The term containing x 4 y 5 will be C(9, 5) x 4 (-2y) 5 = (9!/(5!4!)) x 4 (-2) 5 y 5 The coefficient of which will be 126 -32= -4032
GH
Answered by George H. • Maths tutor
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Using the trigonometric identity for tan(A + B), prove that tan(3x)=(3tan(x)-tan^3(x))/(1-3tan^2(x))

tan(3x)=tan(2x+x), by using the identity for tan(A+B)=(tan(A)+tan(B))/(1-tan(A)tan(B)),tan(3x)=tan(2x+x)=(tan(2x)+tan(x))/(1-tan(2x)tan(x)), using it again for tan(2x),tan(3x)=tan(2x+x)=([(tan(x)+tan(x))/(1-...
IR
Answered by Ivan R. • Maths tutor
11413 Views

a curve is defined by y=2x^2 - 10x +7. point (3, -5) lies on this curve. find the equation of the normal to this curve

equation of tangent is y - y1 = m(x-x1). differentiating y gives us the value of m. so dy/dx = 4x-10. we know x is 3. therefore, dy/dx = m = 2 but we need equation of the normal, which is y-y1=(1/m)(x-x1). 1...
HH
Answered by Huy H. • Maths tutor
3965 Views

The curve C has an equation y = sin(2x)cos(x)^2. Find dy/dx. Find normal to curve at x = pi/3 rad, giving answer in exact form.

Student should use a combination of trigonometric identities, product rule and chain rule to find dy/dx.This can be done by applying product rule, obtainingdy/dx = sin(2x). d[cos(x)^2]/dx + cos(x)^2. d[sin(2...
SC
Answered by Sunchi C. • Maths tutor
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