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1. Find the area under the given curves and given lines:

(i) \(y=x^2\), x=1, x=2 and x-axis

(ii) \(y=x^4\), x=1, x=5 and x-axis

2. Sketch the graph of \(y=\left|x+3\right|\) and evaluate \(\int_{-6}^{0}\left|x+3\right|dx\).

3. Find the area bounded by the curve \(y=sinx\) between x=0 and \(x=2\pi\).

Choose the correct answer in the following Exercises from 4 to 5.

4. Area bounded by the curve \(y=x^3\), the x-axis and the ordinates x=–2 and x=1 is:

(A) –9 (B) \(\frac{-15}{4}\) (C) \(\frac{15}{4}\) (D) \(\frac{17}{4}\)

5. The area bounded by the curve y=x|x|, x-axis and the ordinates x=–1 and x=1 is given by:

(A) 0 (B) \(\frac{1}{3}\) (C) \(\frac{2}{3}\) (D) \(\frac{4}{3}\)