Evaluate \(\int _{ 0 }^{ 1 }{ x^3dx } \), as the limit of a sum.

Evaluate\(\int _{ 1 }^{ 4 }{ ({ 2x }^{ 2 }+3) } \) dx, as the limit of a sum

Evaluate \(\int _{ 0 }^{ x }{ { x }^{ 2 } } \)cos nx dx, where n is a positive integer.

Evaluate: \(\\ \\ \int _{ -1 }^{ 1 }{ { e }^{ -\lambda x }(1-{ x }^{ 2 }) } dx\)

Evaluate \(\int ^\frac {\pi}{2}_{0} \)( sin² x + cos⁴ x ) dx

Evaluate \(\int _{ 0 }^{ 1 }{ { x }^{ 5 }{ (1-{ x }^{ 2 }) }^{ 5 }dx } \)

Evaluate \(\int _{ 0 }^{ 1 }{ { x }^{ 3 }{ (1-x) }^{ 4 }dx } \)

Find the area of the region bounded between the parabola y² = 4ax and its latus rectum.

Find the area of the region bounded between the parabolas y²  = 4x and x² = 4y.

Using integration find the area of the region bounded by triangle ABC, whose vertices A, B, and C are (−1, 1), (3, 2), and (0, 5) respectively