4. Tentukan nilai integral dari soal di bawah ini! a. (3x³-4x² + 5)dx = b. (3x-5)dx = C. c. √ (3x² - 6x'+ 1)dx
Answer (3)
5 ( x − 4 ) ( x + 3 ) = 5 ( x 2 + 3 x − 4 x − 12 ) = 5 ( x 2 − x − 12 ) = 5 x 2 − 5 x − 60
The quadratic equation whose roots are 4 and -3 and leading coefficient is 5 is 5 X 2 − 5 X − 60 = 0 . To derive this, we form factors from the roots, scale by the leading coefficient, and expand. Finally, the equation is written in standard form.
;
•°• Jawaban dari soal-soal tersebut adalah:a.) nilai dari [tex]\sf{\int(3x³ - 4x² + 5)~dx}[/tex] adalah [tex]\underline{\boxed{\red{\sf{\dfrac{3}{4}x⁴ - \dfrac{4}{3}x³ + 5x + C}}}}[/tex],b.) nilai dari [tex]\sf{\int{(3x - 5)}~dx}[/tex] adalah [tex]\underline{\boxed{\red{\sf{\dfrac{3}{2}x² - 5x + C}}}}[/tex],c.) nilai dari [tex]\sf{\int(3x² - 6x + 1)~dx}[/tex] adalah [tex]\underline{\boxed{\red{\sf{x³ - 3x² + x + C}}}}[/tex].[tex] \\ \\ [/tex]Penjelasan dengan langkah-langkah:Soal A[tex]\sf{\int(3x³ - 4x² + 5)~dx}[/tex]= [tex]\sf{\dfrac{3}{3 + 1}x^{(3 + 1)} - \dfrac{4}{2 + 1}x^{(2 + 1)} + 5x + C}[/tex]= [tex]\underline{\boxed{\red{\sf{\dfrac{3}{4}x⁴ - \dfrac{4}{3}x³ + 5x + C}}}}[/tex][tex] \: [/tex][tex]__________________________________________________________________________________________[/tex]Soal B[tex]\sf{\int{(3x - 5)}~dx}[/tex]= [tex]\sf{\dfrac{3}{1 + 1}x^{(1 + 1)} - 5x + C}[/tex]= [tex]\underline{\boxed{\red{\sf{\dfrac{3}{2}x² - 5x + C}}}}[/tex][tex] \: [/tex][tex]__________________________________________________________________________________________[/tex]Soal C[tex]\sf{\int(3x² - 6x + 1)~dx}[/tex]= [tex]\sf{\dfrac{3}{2 + 1}x^{(2 + 1)} - \dfrac{6}{1 + 1}x^{(1 + 1)} + x + C}[/tex]= [tex]\sf{\dfrac{3}{3}x³ - \dfrac{6}{2}x² + x + C}[/tex]= [tex]\underline{\boxed{\red{\sf{x³ - 3x² + x + C}}}}[/tex][tex]~[/tex][tex]__________________________________________________________________________________________[/tex][tex] \\ \\ [/tex] [tex]\blue{\boxed{\colorbox{skyblue}{\rm{- AvR}}}}[/tex]
