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Integrate ∫_(-1)^1 3/√(x+2) dx using the substitution u x+2

Step 1:Replace any obvious in the integral with the substitution u=x+2 ∫_(-1)^1 3/√u dx Step 2: Differentiate the substitution u=x+2 to find an expression for dx (to differentiate multiply by the power and t...
MY
Answered by Micaela Y. • Maths tutor
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Show that the integral ∫(1-2 sin^2⁡x)/(1+2sinxcosx) dx = (1/2) ln2 between the limits π/4 and 0. [5 marks]

First, we use the trig identities: cos2x=cos^2x-sin^2x, cos^2x+sin^2x=1 and sin2x=2sinxcosx to transform the integral to ∫(cos2x)/(1+sin2x)dx. We know that ∫f'(x)/f(x)dx = ln|f(x)|+c, so we let f(x)=1+sin2x....
AC
Answered by Abby C. • Maths tutor
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Write (√(18)+10)/√(2) in the form: p + q√2 [4 marks]

First, simplify √18 by writing it as √(9x2) = √9 x √2 = 3√2. Then, rationalise the denominator by multiplying both top and bottom of the fraction by √2. This gives √2 x √2 = 2 in the denominator, and (3√2+10...
AC
Answered by Abby C. • Maths tutor
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f(x) = 4x^2 + 8x - 5 ; complete the square to find the turning point of f(x).

4x^2 + 8x - 5 = 0 4(x^2 + 2x - (5/4)) = 0 4((x + 1)^2 - 1^2 - (5/4)) = 0 4((x + 1)^2 - (9/4)) = 0 4(x + 1)^2 - 9 = 0 4(x + 1)^2 - 9 = 0 Turning point is at (-1, -9)
CK
Answered by Charlotte K. • Maths tutor
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Solve the simultaneous equations: y=x^2+4x-2, y=x+2

Equations: 1). y=x^2+4x-2 2.)y=x+2 x+2=x^2+4x-2 First put equation 1 in equation 2 0=x^2+3x-4 Make one side of the equation equal to 0 0=(x+4)(x-1) Factorise the equations Equations 3).x+4=0 4). x-1=0 One or...
PA
Answered by Phoebe A. • Maths tutor
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