8. Definite Integrals

Evaluate the following integral:

${\int }_1^4(2x+1)dx$

Given the definite integral $F\left(x\right)={\int }_3^x[t^8-\sin \left(t^4\right)]dt$ , find the derivative $F^{\prime }\left(x\right)$.

Given the definite integral $F\left(x\right)=\int_{12}^{20x}\!\left(h^4+\frac{63h}{\sqrt{h^5}}\right)\,dh$, find the derivative $F^{\prime}\left(x\right)$.

Evaluate the following integral:

${\int }_0^{3}4dx$

Evaluate the following integral:

${\int }_{-1}^2(x^2-3x+2)dx$

Evaluate the following integral:

${\int }_0^1(2x^3-x^2+4x)dx$

Evaluate the following integral:

${\int }_2^3{x}^{\frac{5}{2}}dx$

Evaluate the following integral:

${\int }_1^2\frac{5}{x^2}dx$

Definite integrals Evaluate the following integrals using the Fundamental Theorem of Calculus

∫₁⁸ 8𝓍¹/³ d𝓍

Definite integrals Evaluate the following integrals using the Fundamental Theorem of Calculus

∫₁⁹ 2/(√𝓍) d𝓍

Definite integrals Evaluate the following integrals using the Fundamental Theorem of Calculus

∫¹₁/₂ (t⁻³ ― 8) dt

Definite integrals Evaluate the following integrals using the Fundamental Theorem of Calculus

∫₋₂⁻¹ 𝓍⁻³ d𝓍

Definite integrals Evaluate the following integrals using the Fundamental Theorem of Calculus

∫₁² 3/t dt

Definite integrals Evaluate the following integrals using the Fundamental Theorem of Calculus

∫₁⁴ (𝓍 ― 2)/√𝓍 d𝓍

Definite integrals Evaluate the following integrals using the Fundamental Theorem of Calculus

∫π/₄^³π/⁴ (cot² 𝓍 + 1) d𝓍