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Recall the product rule for differentiation. If y=uv, where u and v are functions defined by functions of x, then we can take the derivative of y as: y'=u'v+v'u () (where ' denotes the derivative) ...
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 p...
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)=...
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...
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)
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