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Evaluate the indefinite integral when the integrand function is tan(x).

To solve this problem we will use a clever substitution to easily integrate and thus obtain the answer.First we can represent tan(x) as its fractional equivalent sin(x)/cos(x), assigning the variable u to co...
JN
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Using Pythagoras' theorem, show that sin^2(x)+cos^2(x)=1 for all x.

Take a right angled triangle with hypotenuse of length 1, and angle at the bottom of the hypotenuse equal to x. We will let o denote the length of the side opposite the angle, and a denote the length of the ...
Answered by • Maths tutor
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Given x = 3sin(y/2), find dy/dx in terms of x, simplifying your answer.

The first step is to find dx/dy in terms of y, which when differentiating comes out as 3/2cos(y/2), so dy/dx in terms of y is the reciprocal of this.The next step is to eliminate the y dependent terms, which...
MA
Answered by Max A. • Maths tutor
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The gradient of a curve is given by dy/dx = 6sqrt(x) + 2. The curve passes through the point (16, 38). Find the equation of the curve.

dy/dx = 6x 1/2 + 2 y = (6 2/3)x 3/2 + 2x + c = 4x 3/2 + 2x + c 38 = (4 16 3/2 ) + (2*16) + c c = 38 - 256 - 32 = -250 y = 4x 3/2 + 2x - 250
FW
Answered by Fraser W. • Maths tutor
5374 Views

How do you integrate (x/(x+1)) dx without using substitution.

A tricky question which is actually really simple if you know the technique and will save a lot of time during the exam. The method is to simply add 1 and minus one to the numerator. so the integral becomes ...
Answered by • Maths tutor
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