Chapter 4: Integration
Section 4.3: Fundamental Theorem of Calculus and the Indefinite Integral
Obtain an explicit rule for the function gx=∫0x11+x2 ⅆx; then show g′x is the integrand evaluated at x.
Control-drag the equation gx=…
Context Panel: Assign Function
gx=∫0x11+t2 ⅆt→assign as functiong
Write the derivative notation g′x
Context Panel: Evaluate and Display Inline
g′x = 1x2+1
The explicit rule for gx and its derivative
Write gx and press the Enter key.
(This displays the explicit rule for gx.)
Context Panel: Differentiate≻With Respect To≻x
→differentiate w.r.t. x
As per the Fundamental Theorem of Calculus, the definite integral defines the antiderivative, so the derivative is the integrand.
The antiderivative of the integrand 1/1+t2 is found by consulting Table 3.10.1
, or by relying on Maple.
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