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Area between curves practice problems

Integrate top minus bottom between the points where the curves cross. 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.

Find the area of the region bounded by \( \displaystyle y = - x^{2} + 4 x + 3 \) and \( \displaystyle y = 3 x + 1 \).

Problem 5.1medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 3 x^{2} + 14 x - 11 \) and \( \displaystyle y = 2 x - 2 \).

Problem 5.2medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - x^{2} - x + 10 \) and \( \displaystyle y = 2 - 3 x \).

Problem 5.3medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 3 x^{2} + 10 x - 1 \) and \( \displaystyle y = - 2 x - 1 \).

Problem 5.4medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - x^{2} - 1 \) and \( \displaystyle y = 2 x - 1 \).

Problem 5.5medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + 5 x + 24 \) and \( \displaystyle y = 3 x \).

Problem 5.6medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + x + 14 \) and \( \displaystyle y = - 3 x - 2 \).

Problem 5.7medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - x^{2} + x + 1 \) and \( \displaystyle y = 3 x + 1 \).

Problem 5.8medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + 6 x - 3 \) and \( \displaystyle y = - 2 x - 3 \).

Problem 5.9medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - x^{2} + x + 2 \) and \( \displaystyle y = x - 2 \).

Problem 5.10medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 3 x^{2} + 10 x - 5 \) and \( \displaystyle y = x + 1 \).

Problem 5.11medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} - 3 x - 1 \) and \( \displaystyle y = - x - 1 \).

Problem 5.12medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 3 x^{2} + 13 x - 11 \) and \( \displaystyle y = 1 - 2 x \).

Problem 5.13medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 3 x^{2} + 17 x - 16 \) and \( \displaystyle y = 2 x + 2 \).

Problem 5.14medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + 7 x - 8 \) and \( \displaystyle y = - 3 x \).

Problem 5.15medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + x + 17 \) and \( \displaystyle y = 1 - 3 x \).

Problem 5.61medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + 3 x + 15 \) and \( \displaystyle y = - x - 1 \).

Problem 5.62medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + 13 x - 17 \) and \( \displaystyle y = x - 1 \).

Problem 5.63medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + 3 x - 6 \) and \( \displaystyle y = - 3 x - 2 \).

Problem 5.64medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + 11 x - 9 \) and \( \displaystyle y = x + 3 \).

Problem 5.65medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 3 x^{2} + 16 x - 11 \) and \( \displaystyle y = x + 1 \).

Problem 5.66medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - x^{2} - 5 x - 1 \) and \( \displaystyle y = - 2 x - 1 \).

Problem 5.67medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + 6 x + 9 \) and \( \displaystyle y = 2 x + 3 \).

Problem 5.68medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + 15 x - 21 \) and \( \displaystyle y = x + 3 \).

Problem 5.69medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + x + 15 \) and \( \displaystyle y = - 3 x - 1 \).

Problem 5.70medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 3 x^{2} + 13 x - 12 \) and \( \displaystyle y = x - 3 \).

Problem 5.71medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 3 x^{2} - 2 x - 3 \) and \( \displaystyle y = x - 3 \).

Problem 5.72medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + 9 x + 7 \) and \( \displaystyle y = 3 x - 1 \).

Problem 5.73medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = - 2 x^{2} + x + 3 \) and \( \displaystyle y = 3 x + 3 \).

Problem 5.74medium✓ Every equation proved

Find the area of the region bounded by \( \displaystyle y = 3 - 2 x^{2} \) and \( \displaystyle y = 2 x - 1 \).

Problem 5.75medium✓ Every equation proved