Evaluate the following definite integrals:
\int_{0}^{3} \left( 4 x + 5\right) dx
\int_{ - 2 }^{0} \left( 10 x + 4\right) dx
\int_{2}^{4} \left( 6 x + 5\right) dx
\int_{3}^{4} \left( - 4 x + 3\right) dx
\int_{ - 4 }^{5} \left( - 8 x + 3\right) dx
\int_{ - 10 }^{ - 6 } \left( - 5 x + 8\right) dx
\int_{ - 2 }^{0} 9 x^{2} dx
\int_{ - 1 }^{3} 9 x^{2} dx
\int_{ - 2 }^{1} \left(x^{2} + 4\right) dx
\int_{ - 1 }^{2} \left( 9 x^{2} + 1\right) dx
\int_{4}^{6} \left( 9 x^{2} + 2 x + 7\right) dx
\int_{ - 4 }^{2} x \left(x - 4\right) dx
\int_{0}^{4} 5 x^{\frac{3}{2}} dx
\int_{ - 3 }^{6} x \left(x + 3\right) \left(x - 6\right) dx
\int_{6}^{11} \sqrt{x - 2} dx
\int_{3}^{6} \left(\sqrt{x - 2} + 5\right) dx
\int_{3}^{4} \left( 2 x + 3\right)^{3} dx
\int_{ - 4 }^{2} \left(\left(x + 2\right)^{3} + 3\right) dx
\int_{1}^{2} \dfrac{x^{5} - x^{ - 2 }}{x^{2}} dx
Consider the function f \left( x \right) = x^2. Find the value of the following:
Consider the function f \left( x \right) = 2 x.
Find the value of \int_{0}^{3} f \left( x \right) dx.
Find the value of \int_{0}^{3} 5f \left( x \right) dx.
Find the value of 5\int_{0}^{3} f \left( x \right)dx.
State the property of definite integrals demonstrated by parts (b) and (c).
Given that \int_{ - 2 }^{7} f \left( x \right) dx = 2, find \int_{ - 2 }^{7} 5 f \left( x \right) dx.
Given that \int_{ - 1 }^{6} f \left( x \right) dx = 3, find \int_{ - 1 }^{6} \left( 9 f \left( x \right) - 2\right) dx.
Consider the function f \left( x \right) = 6 x.
Find the value of \int_{4}^{8} f \left( x \right) dx.
Find the value of \int_{8}^{4} f \left( x \right) dx.
State the property of definite integrals demonstrated by parts (a) and (b).
Given that \int_{4}^{6} f \left( x \right) dx = 3, find the values of the following:
\int_{6}^{4} f \left( x \right) dx
\int_{4}^{6} 3 f \left( x \right) dx
\int_{4}^{6} \left(f \left( x \right) + x\right) dx
Given that \int_{ - 1 }^{2} f \left( x \right) dx = 4 and \int_{2}^{8} f \left( x \right) dx = 8, find the values of the folowing:
\int_{ - 1 }^{8} f \left( x \right) dx
\int_{8}^{ - 1 } f \left( x \right) dx
\int_{ - 1 }^{2} 2 f \left( x \right) dx + \int_{2}^{8} 3 f \left( x \right) dx
Given that \int_{ - 1 }^{3} f \left( x \right) dx = 5 and \int_{2}^{3} f \left( x \right) dx = 2, find the values of the following:
\int_{ - 1 }^{2} f \left( x \right) dx
\int_{3}^{ - 1 } f \left( x \right) dx
2 \int_{ - 1 }^{2} f \left( x \right) dx + \int_{2}^{3} 3 f \left( x \right) dx