Chapter 5: Q12E (page 306)
Evaluate the indefinite integral\(\int {{{\sec }^2}2} \theta d\theta \).
The indefinite integral value of the given equation is\(\int {{{\sec }^2}} 2\theta d\theta = \frac{1}{2}\tan \theta + c\).
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Derivate the function \(g(x) = \int_1^x {\frac{1}{{{t^3} + 1}}} dt\) using the part 1 of the fundamental theorem of calculus.
Evaluate the integral.
\(\int_0^{\pi /4} {\frac{{1 + {{\cos }^2}\theta }}{{{{\cos }^2}\theta }}} d\theta \).
Calculate the area of the region that lies under the curve and above the x-axis.
\({\rm{y = 1 - }}{{\rm{x}}^{\rm{2}}}\)
Evaluate the given integral.
\(\int\limits_0^{\frac{{3\pi }}{2}} {\left| {\sin x} \right|dx} \)
Evaluate the integral.
\(\int_0^{\pi /3} {\frac{{\sin \theta + \sin \theta {{\tan }^2}\theta }}{{{{\sec }^2}\theta }}} d\theta \)
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