Hasil dari [tex]\bf{\int_{-1}^{3}\left(4x^{3}\right)dx+\int_{3}^{4}\left(4x^{3}\right)dx}[/tex] adalah 255
[tex] \: [/tex]
[tex]\boxed{\boxed{\mathbf{A.}} \ \boxed{\mathbf{Pengertian \ Singkat}}}[/tex]
Integral => lawan dari turunan. Jika f(x) turunan pertama dari F(x), maka :
[tex]\boxed{\mathbf{\int_{ }^{ }f(x)dx=F(x)+C}}[/tex]
Rumus yang sering dipakai :
[tex]\boxed{\mathbf{\int_{ }^{ }ax^{n}\ dx=\frac{a}{n+1}x^{n+1}+C}}[/tex]
[tex]\boxed{\boxed{\mathbf{B.}} \ \boxed{\mathbf{Integral \ Tak \ Tentu}}}[/tex]
ada 6 integral tak tentu yang perlu anda ketahui, diantaranya :
[tex]\mathbf{1.\ \ \int_{ }^{ }ax^{n}\ dx=\frac{a}{n+1}x^{n+1}+C;n\ne1}[/tex]
[tex]\mathbf{2.\ \ \int_{ }^{ }\frac{1}{x}\ dx=\ln\ | x |+C}[/tex]
[tex]\mathbf{3.\ \ \int_{ }^{ }\sin x\ dx=-\cos x+C}[/tex]
[tex]\mathbf{4.\ \ \int_{ }^{ }\cos x\ dx=\sin x+C}[/tex]
[tex]\mathbf{5.\ \ \int_{ }^{ }e^{x}\ dx=e^{x}+C}[/tex]
[tex]\mathbf{6.\ \ \int_{ }^{ }a^{x}\ dx=\frac{a^{x}}{\ln a}+C}[/tex]
[tex]\boxed{\boxed{\mathbf{C.}} \ \boxed{\mathbf{Integral \ Tentu}}}[/tex]
ada 6 integral tentu juga yang perlu anda pahami, diantaranya :
[tex]\mathbf{1.\ \ \int_{a}^{b}kf(x)dx=k\int_{a}^{b}f(x)dx}[/tex]
[tex]\footnotesize\mathbf{2.\ \ \int_{a}^{b}f(x)\pm g(x)dx=\int_{a}^{b}f(x)dx\pm\int_{a}^{b}g(x)dx}[/tex]
[tex]\mathbf{3.\ \ \int_{a}^{b}f(x)\ dx=-\int_{b}^{a}f(x)\ dx}[/tex]
[tex]\small\mathbf{4.\ \ \int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx=\int_{a}^{c}f(x)dx}[/tex]
[tex]\mathbf{5.\ \ \int_{a}^{a}f(x)\ dx=0}[/tex]
[tex]\footnotesize\mathbf{6.\ \ \int_{a}^{b}f(x)dx=\int_{a+k}^{b+k}f(x-k)dx=\int_{a-k}^{b-k}f(x+k)dx}[/tex]
Diketahui :
[tex]\bf{\int_{-1}^{3}\left(4x^{3}\right)dx+\int_{3}^{4}\left(4x^{3}\right)dx}[/tex]
Ditanya :
Nilai dari integral adalah...
Jawaban :
[tex]\bf{=\left[x^{4}\right]_{-1}^{3}+\left[x^{4}\right]_{3}^{4}}[/tex]
[tex]\bf{=\left(\left(3\right)^{4}-\left(-1\right)^{4}\right)+\left(\left(4\right)^{4}-\left(3\right)^{4}\right)}[/tex]
[tex]\bf{=\left(81-1\right)+\left(256-81\right)}[/tex]
[tex]\boxed{\bf{=255}}[/tex]
Kelas : 12 SMA
Bab : 1
Sub Bab : Bab 1 - Integral
Kode kategorisasi : 12.2.1
Kata Kunci : Integral.
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Hasil dari [tex]\bf{\int_{-1}^{3}\left(4x^{3}\right)dx+\int_{3}^{4}\left(4x^{3}\right)dx}[/tex] adalah 255
[tex] \: [/tex]
Pendahuluan
[tex]\boxed{\boxed{\mathbf{A.}} \ \boxed{\mathbf{Pengertian \ Singkat}}}[/tex]
Integral => lawan dari turunan. Jika f(x) turunan pertama dari F(x), maka :
[tex]\boxed{\mathbf{\int_{ }^{ }f(x)dx=F(x)+C}}[/tex]
Rumus yang sering dipakai :
[tex]\boxed{\mathbf{\int_{ }^{ }ax^{n}\ dx=\frac{a}{n+1}x^{n+1}+C}}[/tex]
[tex] \: [/tex]
[tex]\boxed{\boxed{\mathbf{B.}} \ \boxed{\mathbf{Integral \ Tak \ Tentu}}}[/tex]
ada 6 integral tak tentu yang perlu anda ketahui, diantaranya :
[tex]\mathbf{1.\ \ \int_{ }^{ }ax^{n}\ dx=\frac{a}{n+1}x^{n+1}+C;n\ne1}[/tex]
[tex]\mathbf{2.\ \ \int_{ }^{ }\frac{1}{x}\ dx=\ln\ | x |+C}[/tex]
[tex]\mathbf{3.\ \ \int_{ }^{ }\sin x\ dx=-\cos x+C}[/tex]
[tex]\mathbf{4.\ \ \int_{ }^{ }\cos x\ dx=\sin x+C}[/tex]
[tex]\mathbf{5.\ \ \int_{ }^{ }e^{x}\ dx=e^{x}+C}[/tex]
[tex]\mathbf{6.\ \ \int_{ }^{ }a^{x}\ dx=\frac{a^{x}}{\ln a}+C}[/tex]
[tex] \: [/tex]
[tex]\boxed{\boxed{\mathbf{C.}} \ \boxed{\mathbf{Integral \ Tentu}}}[/tex]
ada 6 integral tentu juga yang perlu anda pahami, diantaranya :
[tex]\mathbf{1.\ \ \int_{a}^{b}kf(x)dx=k\int_{a}^{b}f(x)dx}[/tex]
[tex]\footnotesize\mathbf{2.\ \ \int_{a}^{b}f(x)\pm g(x)dx=\int_{a}^{b}f(x)dx\pm\int_{a}^{b}g(x)dx}[/tex]
[tex]\mathbf{3.\ \ \int_{a}^{b}f(x)\ dx=-\int_{b}^{a}f(x)\ dx}[/tex]
[tex]\small\mathbf{4.\ \ \int_{a}^{b}f(x)dx+\int_{b}^{c}f(x)dx=\int_{a}^{c}f(x)dx}[/tex]
[tex]\mathbf{5.\ \ \int_{a}^{a}f(x)\ dx=0}[/tex]
[tex]\footnotesize\mathbf{6.\ \ \int_{a}^{b}f(x)dx=\int_{a+k}^{b+k}f(x-k)dx=\int_{a-k}^{b-k}f(x+k)dx}[/tex]
[tex] \: [/tex]
[tex] \: [/tex]
Pembahasan
Diketahui :
[tex]\bf{\int_{-1}^{3}\left(4x^{3}\right)dx+\int_{3}^{4}\left(4x^{3}\right)dx}[/tex]
Ditanya :
Nilai dari integral adalah...
Jawaban :
[tex]\bf{\int_{-1}^{3}\left(4x^{3}\right)dx+\int_{3}^{4}\left(4x^{3}\right)dx}[/tex]
[tex]\bf{=\left[x^{4}\right]_{-1}^{3}+\left[x^{4}\right]_{3}^{4}}[/tex]
[tex]\bf{=\left(\left(3\right)^{4}-\left(-1\right)^{4}\right)+\left(\left(4\right)^{4}-\left(3\right)^{4}\right)}[/tex]
[tex]\bf{=\left(81-1\right)+\left(256-81\right)}[/tex]
[tex]\boxed{\bf{=255}}[/tex]
[tex] \: [/tex]
[tex] \: [/tex]
Pelajari Lebih Lanjut :
[tex] \: [/tex]
[tex] \: [/tex]
Detail Jawaban :
Kelas : 12 SMA
Bab : 1
Sub Bab : Bab 1 - Integral
Kode kategorisasi : 12.2.1
Kata Kunci : Integral.