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Chapter 4: Q. 54 (page 400)

Find a function f that has the given derivative f and value f(c). Find an antiderivative of f by hand, if possible; if it is not possible to anti differentiate by hand, use the Second Fundamental Theorem of Calculus to write down an antiderivative.

f'x=sinx2;f0=0;

Short Answer

Expert verified

The function isFx=鈭�axsint2dt.

Step by step solution

01

Step 1.Given information 

Given function isf'x=sinx2;f0=0;.

02

Step 2.The formula 

The antiderivative of f is Fx=鈭�axftdtFx=鈭�axsint2dtx鈭�[a,b]

Also given that f0=0the antiderivative is,

Fx=鈭�0xsint2dt .

03

Step 3.The solution

The solution isFx=鈭�axsint2dt.

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Most popular questions from this chapter

Suppose f is positive on (鈭掆垶, 鈭�1] and [2,鈭�) and negative on the interval [鈭�1, 2]. Write (a) the signed area and (b) the absolute area between the graph of f and the x-axis on [鈭�3, 4] in terms of definite integrals that do not involve absolute values.

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