Chapter 5: Q27E (page 299)
If \({\rm{f(1) = 12}}\), \({\rm{f'}}\)is continuous, and\(\int\limits_{\rm{1}}^{\rm{4}} {{\rm{f'(x)dx = 17}}} \), what is the value of\({\rm{f(4)}}\)?
\({\rm{f(4) = 29}}\)
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Evaluate the integral.
\(\int_0^{1/\sqrt 3 } {\frac{{{t^2} - 1}}{{{t^4} - 1}}} dt\).
Find the derivative of function \(y\) using the Part 1 of the Fundamental Theorem of Calculus.
\(y = \int_{\sin x}^1 {\sqrt {1 + {t^2}} } dt\)
All continuous functions have derivatives.
Evaluate the integral.
\(\) \(\int\limits_{\rm{0}}^{\rm{4}} {{\rm{(3}}\sqrt {\rm{t}} {\rm{ - 2}}{{\rm{e}}^{\rm{t}}}{\rm{)dt}}} \)
Find the derivative of the function \({g^\prime }(s)\), using part 1 of The Fundamental Theorem of Calculus and integral evaluation.
\(g(s) = \int_5^s {{{\left( {t - {t^2}} \right)}^8}} dt\)
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