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The function f(x) has derivative f′(x)=3x2+6x+1.
Given that the point (1,2) lies on the curve of f(x), find f(x).
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Find ∫6−6x.
A quadratic function f has f′(x)=6−6x and a maximum value of 5.
Find f(x).
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Consider a vehicle moving along a straight road with velocity
for 0≤t≤5 (time in seconds).
Write down, without evaluation, the definite integral that gives the total distance D travelled from t=0 to t=5.
Evaluate∫052+t1000dt.
State, in context, what the numerical value of D represents.
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Consider a function f whose derivative is
Find an expression for f(x).
Given that f(1)=4, determine C.
Write down, without evaluation, the definite integral that gives the area A under the curve y=f(x) between x=0 and x=2.
Evaluate this integral to find the exact value of A.
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