**Question: **a) Estimate the area under f(x) = x^{2}+3 between x = 0 and *x* = 4 using 4 left rectangles.

b) Write, but do not evaluate, an integral that will give the area under the curve in part a.

**Question: **Integrate the following functions:

(a) \(f\left( x \right)=2{{x}^{3}}-3{{x}^{2}}+1\) between 0 and 1

(b) \(f\left( x \right)=6{{x}^{2}}+18x\) between -3 and 0

**Question: **Differentiate the following functions:

(a) \(f\left( x \right)={{x}^{2}}{{\left( 2x+3 \right)}^{5}}\)

(b) \(f\left( x \right)=\frac{1}{{{\left( 4{{x}^{2}}-7 \right)}^{2}}}\)

**Question: **Integrate \(\int{0.4\sqrt{\cos \theta }\sin \theta d\theta }\)

**Question: **Integrate \[\int{4{{\tan }^{2}}x{{\sec }^{2}}xdx}\]

**Question: **Integrate \[\int{4{{\tan }^{2}}x{{\sec }^{2}}xdx}\]

**Question: **Solve the following integral

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