Using integration, find the area of the region bounded between the line x = 2 and the parabola y² = 8x.

Using integration, find the area of the region bounded by the line y – 1 = x, the x – axis and the ordinates x = – 2 and x = 3.

Find the area the region bounded by the parabola y² = 4ax and the line x = a.

Find the area lying above the x - axis and under the parabola y = 4x – x².

Draw a rough sketch to indicate the bounded between the curve y² = 4x and the line x = 3. Also, find the area of this region

Make a rough sketch of the graph of the function y = 4 – x², 0 ≤ x ≤ 2 and determine the area enclosed by the curve, the x - axis and the lines x = 0 and x = 2.

Find the area under the curve above x - axis from x = 0 to x = 2. Draw a sketch of curve also.

Draw the rough sketch of y² + 1 = x, x ≤ 2. Find the area enclosed by the curve and the line x = 2

Draw a rough sketch of the graph of the curve and evaluate the area of the region under the curve and above the x - axis

Sketch the region {(x,y):9x² + 4y² = 36} and the find the area of the region enclosed by it, using integration

Draw a rough sketch of the graph of the function y=2√1–x²,x[0,1] and evaluate the are enclosed between the curve and the x–axis.

Determine the area under the included between the lines x = 0 and x = 1

Using integration, find the area of the region bounded by the line 2y = 5x + 7, x - axis the lines x = 2 and x = 8.

Using definite integrals, find the area of circle x² + y² = a²

Using integration, find the area of the region bounded by the following curves, after making a rough sketch: y = 1 + |x + 1|, x = - 2, x = 3, y = 0.

Sketch the graph y = |x - 5|. Evaluate . What does this value of the integral represent on the graph?

Sketch the graph y = |x + 3|. Evaluate . What does this integral represent on the graph?

Sketch the graph y = |x + 1|. Evaluate . What does the value of this integral represent on the graph?

Draw a rough sketch of the curve xy –3x – 2y – 10 = 0, x - axis and the lines x = 3, x = 4.

Draw a rough sketch of the curve and find the area between x - axis, the curve and the ordinates x = 0, x = π.

Draw a rough sketch of the curve and find the area between x - axis, the curve and the ordinates x = 0, x = π.

Find the area bounded by the curve y = cosx, x - axis and the ordinates x = 0 and x = 2π.

Show that the areas under the curves y = sin x and y = sin 2x between x = 0 and are in the ration 2:3.

Compare the areas under the curves y = cos²x and y = sin² x between x = 0 and x = π.

Find the area bounded by the ellipse and the ordinates x = ae and x = 0, where b² = a² (1 - e²) and e<1.

Find the area of the minor segment of the circle x² + y² = a² cut off by the line .

Find the area of the region bounded by the curve x = at², y = 2at between the ordinates corresponding t = 1 and t = 2

Find the area enclosed by the curve x = 3 cost, y = 2 sint