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volume = SA (3x)³ = (3x)² x 6 27x³ = 9x² x 6 27x³ = 54x² 27x = 54 27x - 54 = 0 27(x - 2) = 0 x - 2 = 0 x = 2 The question asks for the len...

∫(x³+x²+6)dx= ∫x³dx +∫x²dx+∫6dx =x⁴/4 +x³/3 +6x+C.

To complete the square, we need to rearrange the quadratic equation in the form of ax² + bx + c into the form r(x + p)² + q, where our task is to find the values of the unkowns of r,...

We can divide by (cosx)^2 across the identity (sinx)^2 + (cosx)^2 = 1 (which can be derived from properties of the unit circle and a bit of Pythagoras’ theorem) to achieve

[(sinx)^2 / (cosx)^2] + [...