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The main piece of information this question gives us is that the two lines do not cross or touch. From this we can immediately see that we will need to use the discriminant of the quadratic formula b^...

In order to solve this question we simply must substitute x=1 into f(x).

If we carry out this substitution we see that

f(1) = 2(1^3) + (1^3) -5(1) + c = 2(1) + (1) -5(1) + c = 2 + 1  - 5 + c...

sin^2(x) + sin(x) + cos^2(x) + cos(x) = cos(x)sin(x) + cos(x) + sin(x) +1

(sin^2(x) + cos^2(x) =1) Therefore;

1 +sin(x) + cos(x) = cos(x)sin(x) + sin(x) +cos(x) +1

Cancelling out on b...

List Trigonmetric identities which could help to simpilfy integral

Use cos(2x)= Cos²x-sin²x and sin²x=1-cos²x

Sub identity 2 into 1 and rearrange ...