What does it mean to write an integral in its explicit form?The first part of Fundamental Theorem of Calculus gives an abstract way of producing antiderivatives:Write F ( x ) = ∫ 1 x ( t + 1 ) d t in an explicit form. Check that its derivative is indeed x + 1.What does it mean to find an integral in it explicit form? Does it mean to find its anti derivative?

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What does it mean to write an integral in its explicit form?The first part of Fundamental Theorem of Calculus gives an abstract way of producing antiderivatives:Write   F  (  x  )  =      ∫    1    x    (  t  +  1  )  d  t in an explicit form. Check that its derivative is indeed   x  +  1.What does it mean to find an integral in it explicit form? Does it mean to find its anti derivative?

Dominique Holmes · Accepted Answer

Step 1Here you have a &quot;definite integral&quot; with a variable in one of the limits, so you need to find the antiderivative and actually substitute the limits into it. The general antiderivative is   F  (  t  )  =      t    2        /    2  +  t  +  C so when you substitute the limits you get       x    2        /    2  +  x  −  3      /    2.Step 2Edit: Since the general antiderivative is   F  (  t  )  =      t    2        /    2  +  t  +  C, you find your integral by substituting in the limits.That is,       ∫    1    x    (  t  +  1  )  d  t  =  F  (  x  )  −  F  (  1  )  =      x    2        /    2  +  x  +  C  −  (  3      /    2  +  C  )  =      x    2        /    2  +  x  −  3      /    2..This is not really any different than you would do if the upper limit were 2 or 4/3, except that the result depends on the variable x.

What does it mean to write an integral in its explicit form? The first part of Fundamental Theorem

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