Lanjutan Kumpulan Contoh Soal Integral (2)

\begin{array}{ll}\\ \fbox{21}.&\displaystyle \int d\left ( 2x \right )=\end{array}\\ \begin{array}{ll}\\ .\: \: \qquad &a.\quad \displaystyle x+C\\ &b.\quad \displaystyle 2x+C\\ &c.\quad \displaystyle 3x+C\\ &d.\quad \displaystyle 4x+C\\ &e.\quad \displaystyle 5x+C\end{array}.

Jawab:

\displaystyle \int d\left ( 2x \right )=\int 2\: \: dx=2x+C.

\begin{array}{ll}\\ \fbox{22}.&\displaystyle \int 5\: \: d\left ( 2x \right )=\end{array}\\ \begin{array}{ll}\\ .\: \: \qquad &a.\quad \displaystyle 5+C\\ &b.\quad \displaystyle \frac{5}{2}x+C\\ &c.\quad \displaystyle 5x+C\\ &d.\quad \displaystyle 10x+C\\ &e.\quad \displaystyle 25x+C\end{array}.

Jawab:

\displaystyle \int 5\: \: d\left ( 2x \right )=\int5. 2\: \: dx=\int 10\: dx=10x+C.

\begin{array}{ll}\\ \fbox{23}.&\displaystyle \int 6x\: \: d\left ( 3x \right )=\end{array}\\ \begin{array}{ll}\\ .\: \: \qquad &a.\quad \displaystyle 18x^{2}+C\\ &b.\quad \displaystyle 9x^{2}+C\\ &c.\quad \displaystyle 5x^{2}+C\\ &d.\quad \displaystyle 3x^{2}+C\\ &e.\quad \displaystyle 2x^{2}+C\end{array}.

Jawab:

\displaystyle \int 6x\: \: d\left ( 3x \right )=\int 6x. 3\: \: dx=\int 18x\: dx=\displaystyle \frac{18x^{2}}{2}+C=9x^{2}+C.

\begin{array}{ll}\\ \fbox{24}.&\displaystyle \int \left ( 8x^{3}-2x \right )\: \: d\left ( -2x \right )=\end{array}\\ \begin{array}{ll}\\ .\: \: \qquad &a.\quad \displaystyle -16x^{4}+4x^{2}+C\\ &b.\quad \displaystyle 16x^{4}-4x^{2}+C\\ &c.\quad \displaystyle -4x^{4}-2x^{2}+C\\ &d.\quad \displaystyle -4x^{4}+2x^{2}+C\\ &e.\quad \displaystyle 4x^{4}-2x^{2}+C\end{array}.

Jawab:

\begin{aligned}\displaystyle \int \left (8x^{3}-2x \right )\: \: d\left ( -2x \right )&=\int \left ( 8x^{3}-2x \right ).\left (-2\: \: dx \right )=\int \left (-16x^{3}+4x \right )\: dx=\displaystyle -\frac{16x^{4}}{4}+\frac{4x^{2}}{2}+C\\ &=\displaystyle -4x^{4}+2x^{2}+C \end{aligned}.

\begin{array}{ll}\\ \fbox{25}.&\displaystyle \int \left ( x+3 \right )\: \: d\left ( 2x+6 \right )=\end{array}\\ \begin{array}{ll}\\ .\: \: \qquad &a.\quad \displaystyle 4x^{2}+24x+C\\ &b.\quad \displaystyle 2x^{2}+12x+C\\ &c.\quad \displaystyle x^{2}+6x+C\\ &d.\quad \displaystyle 4x^{2}+C\\ &e.\quad \displaystyle x^{2}+C\end{array}.

Jawab:

\begin{array}{|l|l|}\hline \multicolumn{2}{|c|}{\textrm{Alternatif Jawaban}}\\\hline \textrm{Pertama}&\textrm{Kedua}\\\hline \begin{aligned}\displaystyle \int \left ( x+3 \right )\: d\left ( 2x+6 \right )&=\displaystyle \frac{1}{2}\int \left ( 2x+6 \right )\: d\left ( 2x+6 \right )\\ &=\displaystyle \frac{1}{2}\left [ \frac{1}{2}\left ( 2x+6 \right )^{2} \right ]+C\\ &=\displaystyle \frac{1}{4}\left ( 4x^{2}+24x+36 \right )+C\\ &=\displaystyle \frac{4x^{2}}{4}+\frac{24x}{4}+\frac{36}{4}+C\\ &=x^{2}+6x+\underset{C}{\underbrace{9+C}}\\ &=x^{2}+6x+C \end{aligned}&\begin{aligned}\displaystyle \int \left ( x+3 \right )\: d\left ( 2x+6 \right )&=\int \left ( x+3 \right ).\left ( 2\: dx \right )\\ &=\int \left ( 2x+6 \right )\: dx\\ &=\displaystyle \frac{2x^{2}}{2}+6x+C\\ &=x^{2}+6x+C\\ &\\ &\\ & \end{aligned}\\\hline \end{array}.

InsyaAllah dilanjut

 

Tentang ahmadthohir1089

Nama saya Ahmad Thohir, asli orang Purwodadi lahir di Grobogan 02 Februari 1980. Pendidikan : Tingkat dasar lulus dari MI Nahdlatut Thullab di desa Manggarwetan,kecamatan Godong lulus tahun 1993. dan untuk tingkat menengah saya tempuh di MTs Nahdlatut Thullab Manggar Wetan lulus tahun 1996. Sedang untuk tingkat SMA saya menamatkannya di MA Futuhiyyah-2 Mranggen, Demak lulus tahun 1999. Setelah itu saya Kuliah di IKIP PGRI Semarang pada fakultas FPMIPA Pendidikan Matematika lulus tahun 2004. Pekerjaan : Sebagai guru (PNS DPK Kemenag) mapel matematika di MA Futuhiyah Jeketro, Gubug. Pengalaman mengajar : 1. GTT di MTs Miftahul Mubtadiin Tambakan Gubug tahun 2003 s/d 2005 2. GTT di SMK Negeri 3 Semarang 2005 s/d 2009 3. GT di MA Futuhiyah Jeketro Gubug sejak 1 September 2009
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