Luas dibawah Dua kurva dengan GeoGebra

Untuk menghitung luas dibawah dua kurva atau fungsi, kita bisa menggunakan perintah Integral lihat di bagian Perintah-Perintah atau akses Bantuan.

Integral[fungsi f, fungsi g, angka a, angka b]
Integral tertentu dari perbedaan fungsi f(x) - g(x) dari nilai a ke nilai b. Contohnya:
Integral[f(x), fungsi g(x), 1, 2]
Dalam animasi di bawah ini, semua parameter fungsi dan batas-batas fungsi dibuat dinamis dengan bantuan slider/Luncuran. Silahkan anda explorasi contoh berikut dengan menggeser nilai a, b, c,  k, l, m, n, v, atau w.

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The ADDIE Instructional Design Model

Reviewing Indonesian Teachers Training

There are two types of teacher training that conducted by 12 P4TKs and supported by 30 LPMPs, namely face-to-face trainings and e-training. The allocated budget for teacher training in 12 P4TKs is about 180 billion rupiahs (Ditjen PMPTK, 2009). According to national standard of budgeting for 100 hours training, face-to-face training unit cost is about 2 million rupiahs per teacher per training and for e-training is about 3,5 million rupiahs per teacher per training. Thus every year the Ditjen PMPTK will conduct teacher training for about 100,000 teachers per year, so it is believe that it will take more than ten years for disseminating new curriculum standard or teaching methodology to more than a million teachers.

Face-to-face training is conducted either on campus or off campus involving participants from several provinces. This training has several patterns such as 50 hours, 100 hours, 200 hours, and 600 hours which every training group is followed by about 30 participants. For instance, P4TK TK & PLB is able to conduct 50 hours on campus training followed by two groups of 30 participants. On the other hand, e-training is off-campus conducted involving participant from almost all 30 provinces. This training has a specific pattern which is 100 hour for academic writing guidance. The P4TK which has been developing and conducting e-training with national coverage is only P4TK TK & PLB involving more than 5000 participants a year.

Besides unit cost of training and participants, there is an extrinsic factor which is government policy about education quality improvement throughout teacher certification that gives profession incentive up to 100% of main salary to accredited teachers. Obviously, this policy will lead the increase of the national education budget that gives direct implication to the teacher training budget in the future because of limited foreign exchange reserves. It is believe that if global economic crisis will still remain for the next five years, then there will be teacher training budget crisis.

This over viewing about Indonesian teacher training and budgeting condition encourage us to make a breakthrough action to endorse teachers’ quality improvement throughout training in the limited budget condition. In the other words, we should develop teacher training model that has optimum both units cost and number of participant. We can combine the positive aspects of the face-to-face training and e-training respectively, which are the low face-to-face training unit cost and the relative high number of e-training participants, to establish an optimum training model. The convergence face-to-face training and e-training which is called blended training comes from blended learning concept.

P4TK TK & PLB is a P4TK that takes care kindergarten and special needs school teachers

Ditjen PMPTK (2009). Rencana Kerja Anggaran – Kementrian Lembaga Ditjen PMPTK. Government Budgeting System, Software, Jakarta: Direktorat Jenderal Anggaran.


Indonesia is a big country with a population of more than 220 million which 3,423,946 of them are teachers (Ditjen PMPTK, 2010). There are 42 technical institutions (12 P4TKs and 30 LPMPs scattered over 33 provinces dealing with teacher training as training providers under the General Directorate of Quality Improvement of Teachers and Education Personnel (Dijen PMPTK) - National Education Department. There are two types of training conducted by them, namely face-to-face training and e-training. A face-to-face training has smaller unit cost of training rather than e-training, but an e-training involves much bigger participants rather than face-to-face training involves. All the training is funded by the national budget allocated for National Education Department. On the other hand, government has a policy to improve education quality throughout teacher certification which gives profession incentive up to 100% of main salary to accredited teachers. So that there may be a crisis of education budget for teacher training in the future because of limited national budget and increase of budget for teachers’ incentive.

P4TK is a technical unit as a centre of development and empowerment of teachers that has a study field specialization
LPMP is technical unit as an institution of education quality assurance that lies in 30 provinces in Indonesia

Ditjen PMPTK (2010). Laporan berdasarkan status nuptk, retrieved 22 April 2010 from

E-Tivities - Stage 1: Access