Q. nieh, katanya kurang menantang -_-[tex] \int \frac{12x \times 19x^{2} }{4 \times \sqrt{9x + 2x} }.... Question from @misrokhah439

July 2022 1 15 Report

Q. nieh, katanya kurang menantang -_-

[tex] \int \frac{12x \times 19x^{2} }{4 \times \sqrt{9x + 2x} } \: dx[/tex]

no copas
no ngasal
menggunakan cara

nt: yok jawab yok, membazhir poin saya
-_-

Sinogen

Verified answer

Integral~

$\small\boxed{\bf{\int_{ }^{ }\frac{12x\cdot19x^{2}}{4\cdot\sqrt{9x+2x}}\ dx=\boxed{\bf{\frac{114\sqrt{11}x^{4}}{77\sqrt{x}}+C}}}}$

$\:$

Pendahuluan

$\boxed{\boxed{\mathbf{A.}} \ \boxed{\mathbf{Pengertian \ Singkat}}}$

Integral => lawan dari turunan. Jika f(x) turunan pertama dari F(x), maka :

$\boxed{\mathbf{\int_{ }^{ }f\left(x\right)dx=F\left(x\right)+C}}$

Rumus yang sering dipakai :

$\boxed{\mathbf{\int_{ }^{ }ax^{n}\ dx=\frac{a}{n+1}x^{n+1}+C}}$

$\:$

$\boxed{\boxed{\mathbf{B.}} \ \boxed{\mathbf{Integral \ Tak \ Tentu}}}$

ada 6 integral tak tentu yang perlu anda ketahui, diantaranya :

$\mathbf{1.\ \ \int_{ }^{ }ax^{n}\ dx=\frac{a}{n+1}x^{n+1}+C;n\ne1}$

$\mathbf{2.\ \ \int_{ }^{ }\frac{1}{x}\ dx=\ln\ | x |+C}$

$\mathbf{3.\ \ \int_{ }^{ }\sin x\ dx=-\cos x+C}$

$\mathbf{4.\ \ \int_{ }^{ }\cos x\ dx=\sin x+C}$

$\mathbf{5.\ \ \int_{ }^{ }e^{x}\ dx=e^{x}+C}$

$\mathbf{6.\ \ \int_{ }^{ }a^{x}\ dx=\frac{a^{x}}{\ln a}+C}$

$\:$

$\boxed{\boxed{\mathbf{C.}} \ \boxed{\mathbf{Integral \ Tentu}}}$

ada 6 integral tentu juga yang perlu anda pahami, diantaranya :

$\mathbf{1.\ \ \int_{a}^{b}kf\left(x\right)dx=k\int_{a}^{b}f\left(x\right)dx}$

$\footnotesize\mathbf{2.\ \ \int_{a}^{b}f\left(x\right)\pm g\left(x\right)dx=\int_{a}^{b}f\left(x\right)dx\pm\int_{a}^{b}g\left(x\right)dx}$

$\mathbf{3.\ \ \int_{a}^{b}f\left(x\right)\ dx=-\int_{b}^{a}f\left(x\right)\ dx}$

$\small\mathbf{4.\ \ \int_{a}^{b}f\left(x\right)dx+\int_{b}^{c}f\left(x\right)dx=\int_{a}^{c}f\left(x\right)dx}$

$\mathbf{5.\ \ \int_{a}^{a}f\left(x\right)\ dx=0}$

$\footnotesize\mathbf{6.\ \ \int_{a}^{b}f\left(x\right)dx=\int_{a+k}^{b+k}f\left(x-k\right)dx=\int_{a-k}^{b-k}f\left(x+k\right)dx}$

$\:$

Pembahasan

Diketahui :

$\bf{\int_{ }^{ }\frac{12x\cdot19x^{2}}{4\cdot\sqrt{9x+2x}}\ dx}$

Ditanya :

Hasil dari integral tersebut ialah ?

Jawaban :

$\bf{\int_{ }^{ }\frac{12x\cdot19x^{2}}{4\cdot\sqrt{9x+2x}}\ dx}$

$\bf{=\int_{ }^{ }\frac{3\cdot19x^{3}}{\sqrt{11x}}\ dx}$

$\bf{=\int_{ }^{ }\frac{57x^{3}}{\sqrt{11}\cdot x^{\frac{1}{2}}}\ dx}$

$\bf{=\int_{ }^{ }\frac{57x^{\frac{5}{2}}}{\sqrt{11}}\ dx}$

$\bf{=\frac{57}{\sqrt{11}}\cdot\int_{ }^{ }x^{\frac{5}{2}}dx}$

$\bf{=\frac{57\sqrt{11}}{11}\cdot\left(\frac{1}{\frac{7}{2}}\cdot x^{\frac{7}{2}}\right)+C}$

$\bf{=\frac{57\sqrt{11}}{11}\cdot\frac{2}{7}x^{\frac{7}{2}}+C}$

$\bf{=\frac{114\sqrt{11}x^{\frac{7}{2}}}{77}+C}$

$\boxed{\bf{=\frac{114\sqrt{11}x^{4}}{77\sqrt{x}}+C}}$

$\:$

Pelajari Lebih Lanjut :

Contoh soal integral tentu (1) : brainly.co.id/tugas/50510100

Contoh soal integral tentu (2) : brainly.co.id/tugas/50454066

Tentukan ∫(2x^{2} + 5x)^{2} dx : brainly.co.id/tugas/50364777

Integral dari (x^3 +√x) dx : brainly.co.id/tugas/50722822

$\:$

Detail Jawaban :

Kelas : 12 SMA

Bab : 1

Sub Bab : Bab 1 - Integral

Kode kategorisasi : 12.2.1

Kata Kunci : Integral.

6 votes Thanks 8

misrokhah439 keren kak, jawaban ny bener, dan yang jawab cuma kk :D

Sinogen siap ^^ thanks

misrokhah439 :)

misrokhah439 sama sama kk :D

misrokhah439 kak boleh bantu soal saya gak? bingung saya kak :\

misrokhah439 [tex] \displaystyle \sf \int \frac{45yz \times 5xy \times \sqrt{x + 12y} }{ \sqrt{x} \times 2x + 12xz} \: dz[/tex]

nt: ...
https://brainly.co.id/tugas/51266254?utm_source=android&utm_medium=share&utm_campaign=question